Question

if cosθ⁺sinθ=1 prove that cosθ-sinθ=±1

Answer 1

Nice question...,.......

Answer 2

Answer:

Given that cosθ + sinθ = 1

Now Squaring on both sides.

→ cos²θ + sin²θ + 2 cosθ sinθ = 1

1 - sin²θ + 1 - cos²θ + 2 cosθ sinθ = 1

→ 1 + 2 cosθ sinθ = cos²θ + sin²θ

cos²θ + sin²θ - 2 cosθ sinθ = 1

(cosθ - sinθ)² = 1

→ cosθ - sinθ = ±1

Hope it's helpful to all