Question

Verify the identity.
cot(x-pi/2)=-tanx

Answer 1

didnt we already do this?

Answer 2

I believe so, yet I'm still ??????????? about this new one that came at me. Sorry if I annoyed you...

Answer 3

\(\cos(x-\frac{\pi}{2})=\sin(x)\\\sin(x-\frac{\pi}{2})=-\cos(x)\)

So

\(\cot(x-\frac{\pi}{2}) = \frac{\cos(x-\frac{\pi}{2})}{sin(x-\frac{\pi}{2})}=\frac{\sin(x)}{-\cos(x)}=-\frac{\sin(x)}{\cos(x)}=-\tan(x)\)

Answer 4

just thought it was crazy if two people asked the same exact question

Answer 5

if you want to verify the first two lines,

use
\(\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)\)
and
\(\sin(A-B)=\sin(A)\cos(B)-\sin(B)\cos(A)\)

Answer 6

//I hate this class so much omg// :) Thanks!

Answer 7

example

\(\cos(x-\frac{\pi}{2})=\cos(x)\cos(\frac{\pi}{2})+\sin(x)\sin(\frac{\pi}{2})=\cos(x)*0+\sin(x)*1=\sin(x)\)

Answer 8

np