Question

Evaluate

$( \sin\theta + \cos\theta)^{2} + ( \sin\theta - \cos\theta)^{2}$



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Answer 1

Step-by-step explanation:

(sinθ+cosθ)2+(sinθ−cosθ)2 

=(sin2θ+cos2θ+2sinθcosθ)+(sin2θ+cos2θ−2sinθcosθ) 

=(1+2sinθcosθ)+(1−2sinθcosθ) 

=1+2sinθcosθ+1−2sinθcosθ 

=1+1=2 

∴(sinθ+cosθ)2+(sinθ−cosθ)2=2

Answer 2

Answer:

(cosθ+sinθ)2+(cosθ−sinθ)2=cos2θ+sin2θ+2sinθcosθ+cos2θ+sin2θ−2sinθcosθ

=2(cos2θ+sin2θ)

=2(1)=2