Prove the following :

cos θ sin (90° - θ) + sin θ cos (90° - θ) = 1

To prove,

cos θ sin (90° - θ) + sin θ cos (90° - θ) = 1.

We know that,

sin (90 - θ) = cos θ and cos (90 - θ) = sin θ

Solving L.H.S. of the equation, we get :

⇒ cos θ cos θ + sin θ sin θ

⇒ cos² θ + sin² θ

⇒ 1.

Since, L.H.S. = R.H.S.

Hence, proved that cos θ sin (90° - θ) + sin θ cos (90° - θ) = 1.