Question

IF SinTheta+cos Theta=√2 cos theta,then prove that cos theta-sin theta√2 sin theta

Answer 1

Answer:

sinθ+cosθ=−√2cosθ

Explanation:

Here, 
sinθ−cosθ=√2sinθ
⇒sinθ−√2sinθ=cosθ
⇒sinθ(1−√2)=cosθ
⇒sinθ[(1−√2)(1+√21+√2)]=cosθ
⇒sinθ[1−21+√2)=cosθ
⇒sinθ(−1)=(1+√2)cosθ
⇒−sinθ=cosθ+√2cosθ
⇒−sinθ−cosθ=√2cosθ
⇒sinθ+cosθ=−√2cosθ

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