Question

prove that ( sin θ +cos θ )^2 + ( sin θ - cos θ )^2 = 2.​

Answer 1

Answer:

(sinθ+cosθ)

2

+(sinθ−cosθ)

2

=(sin

2

θ+cos

2

θ+2sinθcosθ)+(sin

2

θ+cos

2

θ−2sinθcosθ)

=(1+2sinθcosθ)+(1−2sinθcosθ)

=1+2sinθcosθ+1−2sinθcosθ

=1+1=2

∴(sinθ+cosθ)

2

+(sinθ−cosθ)

2

=2