WEBVTT
1
00:00:03.569 --> 00:00:09.679 A:middle L:90%
Kasan H squared X minus Sign H Squared IX equals
2
00:00:09.679 --> 00:00:12.750 A:middle L:90%
one. And we want to confirm this identity.
3
00:00:14.539 --> 00:00:19.379 A:middle L:90%
So first, over here we see that coastline hx
4
00:00:19.660 --> 00:00:23.550 A:middle L:90%
were given the it equals e to the x plus
5
00:00:24.140 --> 00:00:26.480 A:middle L:90%
east of the negative x all over, too,
6
00:00:27.239 --> 00:00:30.649 A:middle L:90%
and were given that sine h X equals each of
7
00:00:30.649 --> 00:00:33.270 A:middle L:90%
the X minus each of the negative picks all over
8
00:00:33.270 --> 00:00:37.049 A:middle L:90%
too. Someone to start with my left hand side
9
00:00:37.939 --> 00:00:41.820 A:middle L:90%
. So you, uh, coast on h squared
10
00:00:41.829 --> 00:00:48.780 A:middle L:90%
X minus Sign H squared X, and we're gonna
11
00:00:48.780 --> 00:00:52.869 A:middle L:90%
plug in our values. What are givens? So
12
00:00:52.869 --> 00:00:57.579 A:middle L:90%
we have e to the X plus A to the
13
00:00:57.579 --> 00:01:06.030 A:middle L:90%
negative x all over, too. All squared minus
14
00:01:06.140 --> 00:01:10.689 A:middle L:90%
sign which is each of the ex honesty to the
15
00:01:10.689 --> 00:01:19.019 A:middle L:90%
negative X all over too. All squared. So
16
00:01:19.019 --> 00:01:22.060 A:middle L:90%
now we're gonna square the top and bottom. So
17
00:01:22.060 --> 00:01:26.450 A:middle L:90%
have you two the explicit each of the negative x
18
00:01:27.439 --> 00:01:37.030 A:middle L:90%
squared over seeing squared minus e to the x minus
19
00:01:37.040 --> 00:01:42.200 A:middle L:90%
into the negative Becks squared all over two squared.
20
00:01:42.299 --> 00:01:45.340 A:middle L:90%
So I just separated itself in bottom, squared the
21
00:01:45.340 --> 00:01:51.650 A:middle L:90%
boat So now we'll have a common denominator. Ah
22
00:01:52.280 --> 00:01:56.959 A:middle L:90%
two squared which equal sport. I want to square
23
00:01:56.959 --> 00:02:00.180 A:middle L:90%
the top. So I'm gonna use is this formula
24
00:02:00.180 --> 00:02:05.640 A:middle L:90%
here. We're going to the X plus y squared
25
00:02:05.650 --> 00:02:08.909 A:middle L:90%
formula, and that's how I'm going to expand it
26
00:02:09.110 --> 00:02:13.659 A:middle L:90%
to the already more room somewhere. Well, go
27
00:02:13.659 --> 00:02:23.340 A:middle L:90%
down here all over for so we're gonna use top
28
00:02:23.349 --> 00:02:32.199 A:middle L:90%
formula. So have I exit to X first to
29
00:02:32.210 --> 00:02:37.180 A:middle L:90%
e to the X into the negative books, plus
30
00:02:37.189 --> 00:02:42.430 A:middle L:90%
e to the negative to x with the first boil
31
00:02:43.719 --> 00:02:46.169 A:middle L:90%
minus. I'm gonna do the 2nd 1 e two
32
00:02:46.169 --> 00:02:52.400 A:middle L:90%
the two X There's gonna be minus this time,
33
00:02:52.610 --> 00:02:54.830 A:middle L:90%
too. Into the ex into the negative. Becks
34
00:02:57.120 --> 00:03:02.569 A:middle L:90%
. Close. You should be close plus e to
35
00:03:02.569 --> 00:03:09.169 A:middle L:90%
the negative to x, and I'm going to expand
36
00:03:09.180 --> 00:03:13.120 A:middle L:90%
the I want to just to beat the negative and
37
00:03:13.120 --> 00:03:16.169 A:middle L:90%
the second part. So her you need to the
38
00:03:16.169 --> 00:03:20.870 A:middle L:90%
two x plus two e to the X into the
39
00:03:20.870 --> 00:03:24.189 A:middle L:90%
negative Becks. Plus, he's in the negative to
40
00:03:24.189 --> 00:03:31.969 A:middle L:90%
x minus each of two. X plus two e
41
00:03:31.969 --> 00:03:37.189 A:middle L:90%
to the X into the negative picks minus eats in
42
00:03:37.189 --> 00:03:42.860 A:middle L:90%
the negative to ICs. We're in north. These
43
00:03:42.860 --> 00:03:47.900 A:middle L:90%
for a deceased here. Prentiss seasonally and it's all
44
00:03:47.900 --> 00:04:00.659 A:middle L:90%
over for So now we have each of the each
45
00:04:00.659 --> 00:04:03.409 A:middle L:90%
of the two X and this native is it Sue
46
00:04:03.409 --> 00:04:06.990 A:middle L:90%
? It's gonna subtract out. Same with this one
47
00:04:08.110 --> 00:04:11.680 A:middle L:90%
. And this one in Maryland with two into the
48
00:04:11.689 --> 00:04:15.099 A:middle L:90%
ex. He's a negative picks. So we know
49
00:04:15.099 --> 00:04:21.170 A:middle L:90%
that using our exponents properties X to the A Times
50
00:04:21.180 --> 00:04:29.110 A:middle L:90%
exit B equals X to the A plus B So
51
00:04:29.639 --> 00:04:32.430 A:middle L:90%
there's an understood one here and understood one here and
52
00:04:32.680 --> 00:04:35.930 A:middle L:90%
we're gonna add those exponents and one minus one equals
53
00:04:35.939 --> 00:04:42.329 A:middle L:90%
zero. So this E part will become each of
54
00:04:42.339 --> 00:04:45.790 A:middle L:90%
zero, which is one. So the council's out
55
00:04:45.790 --> 00:04:47.160 A:middle L:90%
and that part counts is out. So now we're
56
00:04:47.160 --> 00:04:53.480 A:middle L:90%
left with two plus two only counsel don't the e
57
00:04:53.480 --> 00:04:58.160 A:middle L:90%
court, because that equals zero. So that counsel's
58
00:04:58.160 --> 00:05:00.410 A:middle L:90%
out. And now we look what two plus two
59
00:05:00.410 --> 00:05:03.060 A:middle L:90%
all over four and two plus two equals four over
60
00:05:03.060 --> 00:05:13.259 A:middle L:90%
core and four divided by four equals one. So
61
00:05:13.259 --> 00:05:16.040 A:middle L:90%
now we're gonna go to part B, So we
62
00:05:16.040 --> 00:05:21.660 A:middle L:90%
have one minus tan H squared X equals ticket H
63
00:05:21.660 --> 00:05:26.449 A:middle L:90%
squared X. So we're gonna rearrange it, and
64
00:05:26.449 --> 00:05:28.480 A:middle L:90%
we're gonna at hand to boat. Sorry. So
65
00:05:28.480 --> 00:05:32.329 A:middle L:90%
we get one equal seeking H squared X plus sand
66
00:05:32.329 --> 00:05:36.139 A:middle L:90%
H Squared IX. Someone started the right hand side
67
00:05:36.149 --> 00:05:42.519 A:middle L:90%
so we have seek it were in bloom Seek it
68
00:05:42.529 --> 00:05:55.889 A:middle L:90%
H squared X plus 10 each square dicks. So
69
00:05:55.889 --> 00:06:00.509 A:middle L:90%
we're going to find were given the It's an H
70
00:06:00.740 --> 00:06:09.069 A:middle L:90%
equals son h X over co sign age picks So
71
00:06:09.069 --> 00:06:13.980 A:middle L:90%
I'm gonna switch this apart. Sign h x times
72
00:06:13.980 --> 00:06:18.170 A:middle L:90%
one over co sign Age X. They were given
73
00:06:18.170 --> 00:06:24.620 A:middle L:90%
that sine h X is into the x minus e
74
00:06:25.360 --> 00:06:30.750 A:middle L:90%
the negative picks over two and the one over co
75
00:06:30.750 --> 00:06:34.389 A:middle L:90%
sign. We're just going to flip the fraction so
76
00:06:34.389 --> 00:06:38.399 A:middle L:90%
the denominator becomes the numerator and a new Moretti becomes
77
00:06:38.399 --> 00:06:43.139 A:middle L:90%
the denominator because we're just gonna flip the direction.
78
00:06:43.560 --> 00:06:45.389 A:middle L:90%
So there's two in this to a council out and
79
00:06:45.389 --> 00:06:48.639 A:middle L:90%
we're left with It's the X minus into the negative
80
00:06:48.649 --> 00:06:56.139 A:middle L:90%
books over E to the X plus into the negative
81
00:06:56.149 --> 00:07:00.129 A:middle L:90%
X. So we're going to use that for change
82
00:07:00.129 --> 00:07:08.170 A:middle L:90%
it a little bit Gonna make the smaller over here
83
00:07:11.360 --> 00:07:13.879 A:middle L:90%
. Hopefully you can see that later. We're gonna
84
00:07:13.879 --> 00:07:19.339 A:middle L:90%
do seek it hx so we have seek it H
85
00:07:19.350 --> 00:07:24.970 A:middle L:90%
picks, which is one over co sign a checks
86
00:07:26.860 --> 00:07:29.110 A:middle L:90%
. So we're just gonna flip our coast or infraction
87
00:07:29.329 --> 00:07:32.920 A:middle L:90%
so two over into the ex plus e to the
88
00:07:32.920 --> 00:07:36.920 A:middle L:90%
negative IX ever gonna use that for speaking in a
89
00:07:36.920 --> 00:07:43.889 A:middle L:90%
little? You're right, this Smalling when I was
90
00:07:43.889 --> 00:07:48.069 A:middle L:90%
here. So now we started with the right hand
91
00:07:48.069 --> 00:07:55.180 A:middle L:90%
side. So I'm going to plug in value.
92
00:07:55.180 --> 00:07:58.759 A:middle L:90%
So I'm gonna plug in to over each of the
93
00:07:58.769 --> 00:08:03.959 A:middle L:90%
Ex plus e to the negative Bix squared, plus
94
00:08:03.970 --> 00:08:09.379 A:middle L:90%
the tangent, which will be a to the x
95
00:08:09.550 --> 00:08:16.040 A:middle L:90%
minus into the negative x all over into the ex
96
00:08:16.430 --> 00:08:18.350 A:middle L:90%
close aides in the negative. Becks. False.
97
00:08:18.350 --> 00:08:22.139 A:middle L:90%
Weird. So what is great is sucking bottom.
98
00:08:24.529 --> 00:08:30.939 A:middle L:90%
So it's two squared over You too. The ex
99
00:08:31.029 --> 00:08:37.769 A:middle L:90%
plus into the negative x Not all these squared close
100
00:08:37.860 --> 00:08:46.159 A:middle L:90%
into the x minus e It's in the negative.
101
00:08:46.169 --> 00:08:50.200 A:middle L:90%
Necks all squared over. You need to the xt
102
00:08:50.210 --> 00:08:56.710 A:middle L:90%
plus e to the negative fix all squared. So
103
00:08:56.710 --> 00:09:01.610 A:middle L:90%
explain this for her four and we'll have a common
104
00:09:01.610 --> 00:09:09.340 A:middle L:90%
denominator already. So using the same formula from before
105
00:09:09.830 --> 00:09:16.850 A:middle L:90%
we know that xt plus why squared equals X squared
106
00:09:16.850 --> 00:09:24.379 A:middle L:90%
plus two x y plus y squared. So that's
107
00:09:24.379 --> 00:09:30.309 A:middle L:90%
why I want to expand the denominator when we got
108
00:09:30.309 --> 00:09:37.440 A:middle L:90%
down here. Still her you to the two x
109
00:09:39.529 --> 00:09:43.370 A:middle L:90%
plus two e to the x into the negative x
110
00:09:45.230 --> 00:09:50.440 A:middle L:90%
plus any to the negative to X No numerator is
111
00:09:50.440 --> 00:09:52.740 A:middle L:90%
gonna be the same thing. Soap. Its attraction
112
00:09:52.740 --> 00:09:58.340 A:middle L:90%
so X minus y squared equals X squared minus two
113
00:09:58.340 --> 00:10:05.019 A:middle L:90%
. Ex wife close wars earlier So it's essentially the
114
00:10:05.019 --> 00:10:07.620 A:middle L:90%
same thing. But you have reminders to ex mines
115
00:10:07.620 --> 00:10:11.159 A:middle L:90%
that positive Well, in a perfect stone here,
116
00:10:16.049 --> 00:10:22.879 A:middle L:90%
so four plus e to the two x my last
117
00:10:22.889 --> 00:10:26.159 A:middle L:90%
two e to the X seats of the negative x
118
00:10:26.649 --> 00:10:33.090 A:middle L:90%
plus e to the negative to X. So now
119
00:10:33.090 --> 00:10:35.580 A:middle L:90%
, as we said before, next to the A
120
00:10:35.590 --> 00:10:41.990 A:middle L:90%
terms accidentally equals X to the A plus B So
121
00:10:41.990 --> 00:10:50.309 A:middle L:90%
I'm gonna use it to cancel out this heart right
122
00:10:50.309 --> 00:10:54.879 A:middle L:90%
here. This each of the works and it's it's
123
00:10:54.879 --> 00:11:00.870 A:middle L:90%
a negative X that will become one one because one
124
00:11:00.870 --> 00:11:03.320 A:middle L:90%
minus one is zero and each of the zero power
125
00:11:03.330 --> 00:11:05.210 A:middle L:90%
Anything to zero powers. One Mr. Everything that
126
00:11:05.210 --> 00:11:09.820 A:middle L:90%
happened down here to this part right here. Don't
127
00:11:09.820 --> 00:11:13.240 A:middle L:90%
counsel out because it's one and I will continue to
128
00:11:13.340 --> 00:11:18.190 A:middle L:90%
simple for expression. So you're a four plus into
129
00:11:18.190 --> 00:11:24.190 A:middle L:90%
the two x minus two times long, which is
130
00:11:24.190 --> 00:11:26.570 A:middle L:90%
this too, plus any to the negative to X
131
00:11:28.450 --> 00:11:31.620 A:middle L:90%
all over Agent to X plus two times one,
132
00:11:31.620 --> 00:11:35.549 A:middle L:90%
which is just too Plus he's of the negative to
133
00:11:35.549 --> 00:11:39.759 A:middle L:90%
X, and now four minus two becomes too.
134
00:11:39.750 --> 00:11:48.740 A:middle L:90%
There you bring over the risk numerator no denominated.
135
00:11:48.750 --> 00:11:52.279 A:middle L:90%
We'll have to plus each of the two x plus
136
00:11:52.289 --> 00:11:56.220 A:middle L:90%
. He's the negative to it. And as you
137
00:11:56.220 --> 00:11:58.110 A:middle L:90%
see the neighbor in the denominator of the same So
138
00:11:58.110 --> 00:12:05.570 A:middle L:90%
that equals one which is our look inside. They're
139
00:12:05.570 --> 00:12:09.159 A:middle L:90%
going over to court. See, So we have
140
00:12:09.200 --> 00:12:13.720 A:middle L:90%
co tangent. H swear X minus one equals Ko
141
00:12:13.720 --> 00:12:20.320 A:middle L:90%
seeking h squared X So I'm going to add one
142
00:12:20.320 --> 00:12:22.190 A:middle L:90%
. It's both sides. You have consensual h squared
143
00:12:22.190 --> 00:12:28.649 A:middle L:90%
. It's equals come seek it H Sklar ticks plus
144
00:12:28.649 --> 00:12:31.419 A:middle L:90%
one. And then I'm going to subtract coast seeking
145
00:12:31.429 --> 00:12:35.450 A:middle L:90%
from both sides So we'll have co tangent h squared
146
00:12:35.450 --> 00:12:41.980 A:middle L:90%
X minus coast seeking H Squared IX and I don't
147
00:12:41.980 --> 00:12:46.570 A:middle L:90%
equal one. So that's how ah redefined this.
148
00:12:48.720 --> 00:12:54.440 A:middle L:90%
So I could just solve until you would someone sorry
149
00:12:54.440 --> 00:12:58.250 A:middle L:90%
about left hand side. So you, uh,
150
00:12:58.440 --> 00:13:01.529 A:middle L:90%
coach tangent h squared X minus co seek it.
151
00:13:01.970 --> 00:13:11.139 A:middle L:90%
H squared X equals one. So we're gonna need
152
00:13:11.139 --> 00:13:15.230 A:middle L:90%
co surgeon h X, And that equals one over
153
00:13:15.230 --> 00:13:18.360 A:middle L:90%
tangent A chicks so you can refer back toe problem
154
00:13:18.360 --> 00:13:24.629 A:middle L:90%
be. We know that change it. H x
155
00:13:26.519 --> 00:13:33.730 A:middle L:90%
equals e to the X minus e It's the negative
156
00:13:33.759 --> 00:13:39.429 A:middle L:90%
x over e to the X first e to the
157
00:13:39.429 --> 00:13:43.679 A:middle L:90%
negative picks still Ko Sanja. It would just be
158
00:13:43.679 --> 00:13:48.929 A:middle L:90%
the reciprocal of that. Remember, Not here.
159
00:13:50.019 --> 00:13:54.610 A:middle L:90%
Quotation will just be the reciprocal of that. So
160
00:13:54.610 --> 00:13:58.470 A:middle L:90%
her e to the x plus e to the magnet
161
00:13:58.470 --> 00:14:03.736 A:middle L:90%
picks over easy X minus the needs of the negativity
162
00:14:05.726 --> 00:14:07.177 A:middle L:90%
. We're also Nico seek it. So we have
163
00:14:07.236 --> 00:14:13.157 A:middle L:90%
coast ekin h Squared IX, not a square just
164
00:14:13.157 --> 00:14:20.586 A:middle L:90%
close to get h X and were given that that
165
00:14:20.586 --> 00:14:30.687 A:middle L:90%
equals won over. Sign A chicks so we know
166
00:14:30.687 --> 00:14:39.756 A:middle L:90%
that sign h x equals e to the X minus
167
00:14:39.917 --> 00:14:48.376 A:middle L:90%
e to the negative x all over too. SoCo
168
00:14:48.376 --> 00:14:50.636 A:middle L:90%
seek It will just be the reciprocal of that.
169
00:14:56.226 --> 00:15:03.917 A:middle L:90%
So, huh two over each of the ex minus
170
00:15:03.927 --> 00:15:09.017 A:middle L:90%
e to the negative picks we're gonna use wasn't useful
171
00:15:09.017 --> 00:15:13.557 A:middle L:90%
are for solving. I want to make you smile
172
00:15:15.927 --> 00:15:20.437 A:middle L:90%
, but you can still see so early, huh
173
00:15:20.927 --> 00:15:26.917 A:middle L:90%
? Back to our left hand side when there is
174
00:15:26.917 --> 00:15:33.826 A:middle L:90%
this part. So you, uh, coat agent
175
00:15:33.826 --> 00:15:39.706 A:middle L:90%
h X squared minus co seek it. H squared
176
00:15:39.706 --> 00:15:45.126 A:middle L:90%
X We're gonna plug in our values. You have
177
00:15:45.126 --> 00:15:48.527 A:middle L:90%
code Sanja, which is e to the X place
178
00:15:48.537 --> 00:15:54.076 A:middle L:90%
e to the negative X over e to the x
179
00:15:54.126 --> 00:16:00.236 A:middle L:90%
minus into the negative picks all squared mon Asarco,
180
00:16:00.236 --> 00:16:03.870 A:middle L:90%
seek it which is to over into the X minus
181
00:16:03.879 --> 00:16:07.710 A:middle L:90%
ease of the negative x and there's all squared also
182
00:16:07.659 --> 00:16:11.509 A:middle L:90%
. So now we're going to expand our numerator denominator
183
00:16:11.519 --> 00:16:14.460 A:middle L:90%
. So you have e to the X plus e
184
00:16:14.720 --> 00:16:19.879 A:middle L:90%
to the negative picks squared over B to the X
185
00:16:19.879 --> 00:16:26.970 A:middle L:90%
minus e to the negative X squared waas two squared
186
00:16:26.799 --> 00:16:33.070 A:middle L:90%
over you to the ex minus e to the negative
187
00:16:33.080 --> 00:16:40.019 A:middle L:90%
. Becks squared. So now we can expand.
188
00:16:40.320 --> 00:16:42.129 A:middle L:90%
We know that our denominator will be the We have
189
00:16:42.129 --> 00:16:47.230 A:middle L:90%
a common denominator. It's everybody's the same formula as
190
00:16:47.230 --> 00:16:52.750 A:middle L:90%
before the x minus y squared, which equals X
191
00:16:52.909 --> 00:16:59.799 A:middle L:90%
squared minus two x y plus y squared. That's
192
00:16:59.799 --> 00:17:11.680 A:middle L:90%
when we used to experience the denominated still her e
193
00:17:11.769 --> 00:17:15.559 A:middle L:90%
to the two IX minus to each of the exceeds
194
00:17:15.559 --> 00:17:19.289 A:middle L:90%
of the negative x plus e to the negative to
195
00:17:19.289 --> 00:17:25.660 A:middle L:90%
ics. No need to expand our numerator and went
196
00:17:25.660 --> 00:17:30.319 A:middle L:90%
to the same thing. So expose y squared equals
197
00:17:30.630 --> 00:17:34.869 A:middle L:90%
x cleared plus to explore, plus y squared.
198
00:17:37.559 --> 00:17:40.029 A:middle L:90%
And that's what I'm gonna use to expand my numerator
199
00:17:45.160 --> 00:17:49.650 A:middle L:90%
. So her e to the two works list to
200
00:17:49.910 --> 00:17:55.009 A:middle L:90%
each of the ex feats of the negative picks plus
201
00:17:55.019 --> 00:18:00.049 A:middle L:90%
e to the negative to ICs and minus two squared
202
00:18:00.049 --> 00:18:07.079 A:middle L:90%
, which equal sport. So now we'll have We're
203
00:18:07.079 --> 00:18:11.410 A:middle L:90%
gonna look here at this e to the X,
204
00:18:11.410 --> 00:18:14.140 A:middle L:90%
and it's a negative X as we know before exiting
205
00:18:14.150 --> 00:18:18.640 A:middle L:90%
a times exit B equals X to the A plus
206
00:18:18.650 --> 00:18:23.579 A:middle L:90%
B so you can see the We haven't understood one
207
00:18:23.579 --> 00:18:30.220 A:middle L:90%
in front of the ex here, So when one
208
00:18:30.220 --> 00:18:33.569 A:middle L:90%
is one is zero and e to the zero equals
209
00:18:33.579 --> 00:18:37.589 A:middle L:90%
one. So this little castle out and the same
210
00:18:37.589 --> 00:18:42.019 A:middle L:90%
thing Same exact thing with that one. I'm just
211
00:18:42.019 --> 00:18:47.009 A:middle L:90%
gonna experiment and Raider units of two x plus any
212
00:18:47.009 --> 00:18:52.609 A:middle L:90%
to the negative to its minus four all over into
213
00:18:52.609 --> 00:18:56.000 A:middle L:90%
the to Alex plus E to the negative to ics
214
00:19:00.279 --> 00:19:03.859 A:middle L:90%
minus two. I was to have a plus to
215
00:19:03.859 --> 00:19:07.410 A:middle L:90%
love here right here for that plus two. So
216
00:19:07.410 --> 00:19:11.170 A:middle L:90%
it's become each of the two works plus into the
217
00:19:11.170 --> 00:19:17.400 A:middle L:90%
negative to X minus two all over the two.
218
00:19:17.400 --> 00:19:19.789 A:middle L:90%
The two x plus He's in the negative two works
219
00:19:21.779 --> 00:19:25.589 A:middle L:90%
minus two and in the marina denominator of the same
220
00:19:25.980 --> 00:19:26.990 A:middle L:90%
logical one