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

Question

Philoid · Accepted Answer

We are given that: sin θ = cos (θ – 45°)

∴We can rewrite it as: cos (90° – θ ) = cos (θ – 45°)

On comparing both sides, we get,

90° – θ = θ – 45°

⇒ θ + θ = 90° + 45°

⇒ 2θ = 135°

⇒ θ = 65.5°