Question

If cos theta + sin theta= 1, prove that cos theta-sin theta = +-1.

answer fast plz...
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Answer 1

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Answer 2

Given that, cosθ + sinθ = 1

⇒ (cosθ + sinθ)² = 1²

⇒ cos²θ + sin²θ + 2 sinθ cosθ = 1

⇒ 1 + 2 sinθ cosθ = 1

⇒ 2 sinθ cosθ = 0

⇒ sinθ cosθ = 0

Now, (cosθ - sinθ)²

= (cosθ + sinθ)² - 4 sinθ cosθ

= 1² - (4 × 0)

= 1 - 0

= 1

⇒ (cosθ - sinθ)² = 1

⇒ cosθ - sinθ = +_ 1

Hence, proved.