Question

If cosθ = sin60° and θ is an acute angle find the value of 1- 2 sin²θ

Answer 1

cosθ = sin60°
⇒ cosθ = `sqrt(3)/(2)`
⇒ cosθ = cos30°
⇒ θ = 30°
Now,
1 - 2sin²θ 
= 1 - 2sin²30°

= `1 - 2(1/2)^2`

= `1 - 2 xx (1)/(4)`

= `1 - (1)/(2)`

= `(1)/(2)`.