Question

Prove : 

(1 - cos2θ) csc2θ  =  1

​

Answer 1

Solution :

Let A = (1 - cos2θ) csc2θ and B = 1.

A = (1 - cos2θ) csc2θ

Because sin2θ + cos2θ = 1, we have

sin2θ = 1 - cos2θ

Then,

A = sin2θ ⋅ csc2θ

A = sin2θ ⋅ (1/sin2θ)

A = sin2θ /sin2θ

A = 1

A = B (Proved)