Question

If 2θ + 45° and 30° – θ are acute angles, find the degree measure of θ satisfying sin (2θ + 45°) = cos (30° – θ)

Answer 1

Here 2θ + 45° and 30° – θ are acute angles:

We know that (90 – θ) = cos θ

sin (2θ + 45°) = sin (90 – (30 – θ))

sin (2θ + 45°) = sin (90 – 30 + θ)

sin (20 + 45°) = sin (60 + θ)

On equating sin of angle of we get

2θ + 45 = 60 + θ

2θ – θ = 60 – 45

θ = 15°