Question

if sin theta + cos theta = √2 cos theta, then prove that cos theta - sin theta =√2sin theta

Answer 1

Given that sin theta +cos theta =root 2cos theta
Squaring both the sides
Sin sq.theta +cos sq. Theta+2sin theta cos theta=2cossq. theta
Bringing cos²Ф and sin²Ф to the left hand side
2sinФcosФ=cos²Ф-sin²Ф

2 sinФcosФ=(cosФ+sinФ)(cosФ-sinФ)
2 sinФcosФ=(√2cosФ)(cosФ-sinФ)
Now take out the value of cosФ-sinФ from it
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