Question

If cosA-sinA=√2sinAfind cosA+sinA

Answer 1

cosA-sinA = √2sinA

squaring both side
⇒(cosA - sin A)² = (√2sinA)²

CosA²+ sinA²- 2sinAcosA = 2 sin²A
=>
1-sinA² +1-CosA²-2sinAcosA= 2sin²A
=>
2 -2sin²A = sin²A + CosA²+ 2sinAcosA
=>
2(1 - sin²A )= (cosA+sinA)²
=>
(cosA+sinA)² = 2 cosA
=>
CosA+ sinA = √2 cosA

Hope it's helpful for you ☺✌