Q. 424.5( 6 Votes )

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

Answer :

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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