Question

If sin θ = cos (θ – 45°), where θ and θ – 45° are acute angles, find the degree measure of θ.

Answer 1

sin θ = cos (θ – 45°)

cos θ = cos (90 – θ)

cos (θ – 45°) = sin (90° – (θ – 45°)) = sin (90 – θ + 45°)

sin θ (135 – θ)

θ = 135 – θ

2θ = 135

∴ θ = `135^circ/2`