Question

Cos theta +sin theta=√2 . Then prove cos theta-sin theta=√2sin theta

Answer 1

Let θ = x

cos x  + sin x =  √2 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

 √2 sinx = cosx - sinx

Answer 2

Answer:

Your answer attached in the photo