Prove that if then .

To prove:

Let x = cos θ

⇒ θ = cos^-1x

For x = 1/2, θ = 60° and for x = 1, θ = 0°

Hence as 1/2 ≤ x ≤ 1 then 0° ≤ θ ≤ 60°

The LHS will become

Now 1 – cos²θ = sin²θ

We know that and

We know that cos (A – B) = cos A cos B + sin A sin B

Hence proved