Question

If cos2θ = sin4θ, where 2θ and 4θ are acute angles, then find the value of θ.

Answer 1

cos 2θ = sin 4θ …(1)

We know that,

sin( 90° – θ) = cos θ

So, equation (1) can be written as

sin (90° – 2θ) = sin 4θ

On comparing both sides

90° – 2θ = 4θ

90° = 4θ + 2θ

6θ = 90°

or θ = 15°

The value of θ is 15°