Question

Verify the following –

(i) (cos(90° - θ)sin(90° - θ))/tan(90° - θ) = sin²θ

(ii) (sincos(90° - θ)cosθ)/sec(90° - θ) + (cossin(90° - θ)sinθ)/cosec(90° - θ) = sinθcosθ

Answer 1

(i) LHS = (cos(90° - θ)sin(90° - θ))/tan(90° - θ) 

= sin²θ

= R.H.S.

(ii) LHS = (sincos(90° - θ)cosθ)/sec(90° - θ) + (cossin(90° - θ)sinθ)/cosec(90° - θ)

= sin³ θ cos θ + cos³ θ sin θ

= sin θ cos θ (sin² θ + cos² θ) [∵ sin² θ + cos² θ = 1]

= sin θ cos θ

= R.H.S