# If cosθ + sinθ = 1, then prove that cosθ – sin θ = ± 1.

Given: cos +sin=1

On squaring both the sides, we get

(cos θ +sin θ)2 =(1)2

cos2 θ + sin2 θ + 2sinθ cos θ = 1

cos2 θ + sin2 θ = cos2 θ + sin2 θ – 2sinθ cos θ

[ cos2 θ + sin2 θ = 1]

cos2 θ + sin2 θ = (cosθ – sinθ)2

[ (a b)2 = (a2 + b2 – 2ab)]

1 = (cos θ sin θ)2

(cos θ sin θ) = ±1

Hence Proved

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