Question

If sin θ + cos θ = 1 and 0° ≤ θ ≤ 90°, then the possible values of θ are ______.

Answer 1

If sin θ + cos θ = 1 and 0° ≤ θ ≤ 90°, then the possible values of θ are 0° and 90°.

Explanation:

Square both sides: (sin θ + cos θ)² = 1 

⇒ sin²θ + cos²θ + 2 sin θ cos θ = 1 

⇒ 1 + 2 sin θ cos θ = 1 

⇒ 2 sin θ cos θ = 0 

⇒ sin²θ = 0

For 0° ≤ θ ≤ 90°, sin²θ = 0 gives 2θ = 0° or 180°, so θ = 0° or 90°. 

Both satisfy the original equation sin 0° + cos 0° = 1 and sin 90° + cos 90° = 1.