Prove that (i) (sin(180° - θ)cos(90° + θ)tan(270° - θ)cot(360° - θ))/((sin(360° - θ)cos(360° + θ)sin(270° - θ)cosec(-θ) = - 1

Question

Prove that

(i) \(\frac{sin(180°-\theta)cos(90°+\theta)tan(270°-\theta)cot(360°-\theta)}{si(360°-\theta)cos(360°+\theta)sin(270°-\theta)cosec(-\theta)}\) = - 1

(ii) sin θ.cos{sin(\(\frac{\pi}{2}\) – θ).cosec θ + cos(\(\frac{\pi}{2}\) – θ).sec θ} = 1

Answer 1

(i) \(\frac{sin(180°-\theta)cos(90°+\theta)tan(270°-\theta)cot(360°-\theta)}{si(360°-\theta)cos(360°+\theta)sin(270°-\theta)cosec(-\theta)}\) = - 1

LHS = \(\frac{sin(180°-\theta)cos(90°+\theta)tan(270°-\theta)cot(360°-\theta)}{si(360°-\theta)cos(360°+\theta)sin(270°-\theta)cosec(-\theta)}\)

(ii) sin θ.cos{sin(\(\frac{\pi}{2}\) – θ).cosec θ + cos(\(\frac{\pi}{2}\) – θ).sec θ} = 1

LHS = sin θ.cos{sin(\(\frac{\pi}{2}\) – θ).cosec θ + cos(\(\frac{\pi}{2}\) – θ).sec θ}