Question

How do you prove `\sin ( \frac { \pi } { 2} - x ) \cot ( \frac { \pi } { 2} + x ) = - \sin x`?

Answer 1

Refer to explanation below.

Explanation:

As `sin(pi/2-x)=cosx and cot(pi/2+x)=-tanx`

We have, `LHS=sin(pi/2-x)*cot(pi/2+x)`

`=cosx*(-tanx)`

`=cosx*(-sinx/cosx)=-sinx=RHS`