Question

Ans. :(C)
What is the procedure of doing this question ??

Answer 1

Answer:

cos2θ=1-2sin^2θ

2sin^2θ=1+ cos2θ

sin^2θ= (1+ cos2θ)/2

Answer 2

For this, we may remember the trigonometric compound angle formula given below.

cos(A + B) = cosA · cosB - sinA · sinB

Here, let A = B = θ. So,

     cos(θ + θ) = cosθ · cosθ - sinθ · sinθ

⇒  cos(2θ) = cos²θ - sin²θ

⇒  cos(2θ) = cos²θ - (2sin²θ - sin²θ)

⇒  cos(2θ) = cos²θ - 2sin²θ + sin²θ

⇒  cos(2θ) = sin²θ + cos²θ - 2sin²θ

⇒  cos(2θ) = 1 - 2sin²θ                       [∵ sin²θ + cos²θ = 1]

⇒  2sin²θ = 1 - cos(2θ)

⇒  sin²θ = [1 - cos(2θ)] / 2

Thus we get that option (C) is correct.