00:01
So it looks like you want to prove this identity.
00:05
So we have secan of t times co -sicant of t times tangent of t, plus cotangent of t.
00:15
And we want to prove that that is equal to secant squared of t plus co -cant squared of t.
00:25
And so i'm going to leave the right side alone, and i'm going to make the left side turn into the right side.
00:30
And i will tell you some justification for why we can do what we can do.
00:34
So i'm going to use the reciprocal identity, and i'm going to change these two functions like so.
00:44
And i'm also going to change the tangent function using the tangent identity into sine of t over cosine of t.
00:53
And i'm going to change this cotangent function by the cotangent identity.
00:58
And oops, and i forgot to rate the s there.
01:00
And the cotangent of t is cosine of t divided by the sign of t and this one i'm just going to leave alone so again i use reciprocal identity here i don't know if you have to put your reasons down but that's reciprocal identity for here and here and this one we call tangent identity and we call this one cotangent identity well now i'm going to distribute and so when i distribute i'll have sign of t over and i normally would just do a reduction but i have cosine squared of t times sine of t, which you can see what's going to happen there.
01:38
And then when i distribute here, i'm going to have the cosine of t on top, and i'm going to have the cosine of t times the sine squared of t...