Question

Can anybody help me verifying this identity:

cot(x-π/2) = -tan x

Answer 1

\[\begin{align*}
\cot\left(x-\frac{\pi}{2}\right)&=\frac{\cos\left(x-\dfrac{\pi}{2}\right)}{\sin\left(x-\dfrac{\pi}{2}\right)}\\\\
&=\frac{\cos x\cos\dfrac{\pi}{2}+\sin x\sin\dfrac{\pi}{2}}{\sin x\cos\dfrac{\pi}{2}-\cos x\sin\dfrac{\pi}{2}}\\\\
&=\frac{\sin x}{-\cos x}\\\\
&=-\tan x
\end{align*}\]