Question

If sin 3θ = cos (θ – 6°) where 3θ and θ − 6° are acute angles, find the value of θ.

Answer 1

3θ, θ – 6 are an acute angle

We know that sin (90 – θ) = cos θ

sin 3θ = sin (90 – (θ - 6°))

sin 3θ = sin(90 – θ + 6°)

sin 3θ = sin (96° - θ)

3θ = 96° – θ

4θ = 96°

`θ = 96^@/4`

`θ = 24^@`