Question

Prove the identity cosec theta costheta 2 1 cos theta 1+cos theta

Answer 1

Answer:

Step-by-step explanation:

To Prove: (Cosecθ - Cotθ)² = 1 - Cosθ/1+Cosθ

L.H.S:

(Cosecθ - Cotθ)²  

= (1/Sinθ - Cosθ/Sinθ)²

=  (1 - Cosθ)²/Sin²θ

= (1 - Cosθ)²/ 1 - Cos²θ  (∵ Sin²θ = 1 - Cos²θ)

= (1 - Cosθ)² / (1 + Cosθ)(1-Cosθ) (∵ denominator of form a² - b² = (a+b)(a-b))

= (1 - Cosθ)(1 - Cosθ) / (1 + Cosθ)(1 - Cosθ)

= 1 - Cosθ / 1 + Cosθ

= R.H.S

Hence proved.