Question

Verify the identity cot(theta - pi/2)= -tan(theta) .

Answer 1

Use these facts:\[
\tan x = \frac{\sin x}{\cos x} \\
\\
\cot x = \frac{\cos x}{\sin x} \\
\sin (x - \pi/2) = \sin (-( \pi/2 - x)) = -\sin (\pi/2 - x)=-\cos x \\
\cos( x - \pi/2) = \cos( -(x - \pi/2)) = \cos( \pi/2 - x ) = \sin x
\]

Answer 2

ok but I got stuck on how to start he problem then when I attempted to work it out it looks so wrong