if cos theta + sin theta =root2 cos theta prove that cos theta - sin theta =root 2 sin theta

 

 let theta = x

cos x  + sin x = root2 cos x

squaring on both side, we get......

cos2x + sin2x + 2cosxsinx = 2cos2x

2sinxcosx = 2cos2x - cos2x - sin2x

2sinxcosx = cos2x - sin2x

2sinxcosx = (cosx+sinx) (cosx - sinx)

2sinxcosx = (root2 cosx) (cosx - sinx)

2sinxcosx/root2 cosx = cosx - sinx

root2 sinx = cosx - sinx

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