Question

verify the trigonometry question

Answer 1

hope this helps you☺️

Answer 2

Cos (90-theta) = sin theta

tan theta = sin theta/cos theta

cot (90-theta) = tan theta.

Now,
LHS =

$\frac{ \cos( \alpha ) \cos(90 - \alpha ) }{ \cot(90 - \alpha ) } \\ \\ = \frac{ \cos( \alpha ) \sin( \alpha ) }{ \tan( \alpha ) } \\ \\ = \frac{ \cos( \alpha ) \sin( \alpha ) }{ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } } \\ \\ \ = cos( \alpha ) \times \cos( \alpha ) \\ \\ = {cos}^{2} \alpha$

Hope it helps.