1.

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

Answer»

sin2θ +cos2θ +2sinθ cosθ =1

1+2sinθ cosθ =1

2sinθ cosθ=0

1-2sinθ cosθ=1

sin2θ +cos2θ-2sinθ cosθ=1

(cosθ -sinθ)2=1

cosθ -sinθ=±1



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