Question

Verify the identity.

cotx minus pi divided by two. = -tan x

Answer 1

\[\cot (x-\Pi/2)=-tanx\]

Answer 2

familiar with Cofunctions Identities?

Answer 3

you also need to familiar with negative angle identities
\[\rm \sin(-x) = -\sin(x) ~~~\color{red}{odd}\]\[\rm \cos(-x)= \cos(x)~~~~~\color{red}{even}\]\[\rm Tan(-x)=-\tan(x)~~\color{red}{odd}\]

Answer 4

\[\rm \cot (x-\frac{\pi}{2} )~ can ~be~written~as~\cot (-\frac{\pi}{2}+x)\]
now first take out the negative sign and then use Cofunctions identity
here is the link if you don't know about it
http://www.analyzemath.com/trigonometry/trigonometric_formulas.html