Question

(tan²θ)(1/1-cosθ + 1/1+cosθ)

Answer 1

Answer:

L.H.S. = tan2 θ/(sec θ – 1)2

= (sin2 θ/cos2 θ)/(1/cos θ – 1) (∵ tan θ = sin θ/cos θ)

= (sin2 θ/cos2 θ)/(1 – cos θ)2/cos2 θ) (∵ sec θ = 1/cos θ)

= sin2 θ/(1 – cos θ)2 [∵ sin2 θ = 1 – cos2 θ]

= (1 – cos2 θ)/(1 – cos θ)2

= (1 – cos θ)(1 + cos θ)/(1 – cos2 θ)2 {∵ a2 – b2 = (a + b)(a – b)}

= 1 + cos θ/1 – cos θ

= R.H.S.