Question

If (cos theta-sin theta)=root of 2 sin theta,prove that cos theta +sin theta = root of 2 cos theta

Answer 1

square the first expression eliminate 2sin∅cos∅ from it.. then write in the form of (cos∅+sin∅)²
(a-b)²=(a+b)²–4ab use like this

Answer 2

Trigonometry,

We have,
using e insted of theta ok,
cose - sine = √2sine

Have to prove that,
cose + sine = √2cose.

Now,
cose - sine = √2sine

= cose = √2sine + sine

= cose = (√2 + 1)sine

= cose/(√2 + 1) = sine

= {cose×(√2 - 1)}/{(√2)²-1} = sine

= √2cose - cose = sine

= √2cose = sine + cose [ proved ]

That's it
Hope it helped (≧∇≦)b