Question

If cos -sin = root2(sin) then prove that cos+sin = root2(cos)

Answer 1

cos-sin =√2 sin

squaring both sides

(cos-sin)²= (√2sin)²

cos²+sin²-2cossin = 2sin²

cos²= 2sin²-sin²+2 cos sin

cos² = sin²+2cos sin

Adding cos both sides

cos²+cos² = sin²+2cos sin +cos²

2cos² = (sin+cos)²

√(2cos²) = sin +cos

√2 cos = cos + sin

Hope it helps !

Answer 2

Answer:

Step-by-step explanation:

Cos - sin = √2 sin

Cos = √2sin + sin

Cos = sin (√2 + 1)

Cos (√2 - 1) = sin (√2 + 1) (√2 - 1)

√2cos - cos = sin (2 - 1)

√2cos - cos = sin

Sin = √2cos - cos

Sin + cos = √2cos