Question

Prove the following:

sin θ sin (90° − θ) − cos θ cos (90° − θ) = 0

Answer 1

We have to prove sin θ sin (90° − θ) − cos θ cos (90° − θ) = 0

Left-hand side

`= sin theta.sin(90^@ - theta) - cos theta.cos(90^@ - theta)`

`=  sin theta.cos theta - cos thete.sin theta`

`= sin theta (cos theta -cos theta)`

= 0

=Right hand side

Proved