Question

If sinθ = cos(θ - 45°),where θ is acute, find the value of θ.

Answer 1

We have

sinθ = cos(θ - 45°)

⇒ cos(90° − θ) = cos(θ − 45°) 

Comparing both sides, we get

90° − θ = θ − 45° 

⇒ θ + θ = 90° + 45° 

⇒ 2θ = 135° 

⇒ θ = (135/2) ° 

∴ θ = 67.5°