Question

if cosA+sinA = √2 cosA, prove that cosA-sinA = √2 sinA.

Answer 1

HELLO DEAR,

cosA+sinA=√2 cos A

SQUARING Both side

we get,

cos²A +sin²A + 2cosA sinA =2cos²A

=> 2cosAsinA=2cos²A- cos²A - sin²A

=> 2cosAsinA =cos²A-sin²A

[adding both side "sin²A"]

=> 2cosAsinA +sin²A =cos ²A -sin²A + sin²A

=> sin²A+sin²A=cos²A+sin²A -2cosAsinA

=> cos²A+sin²A -2cosAsinA =sin²A+sin²A

=> (cosA-sinA)² = 2sin²A

=> cos A -sinA =√2sinA

I HOPE ITS HELP YOU DEAR,
THANKS