Question

If sinA+cosA=root2cosA then prove cosA-sinA=root2sinA​

Answer 1

`\cos A - \sin A = √(2) \sin A` (Proved)

Explanation:

We are given that
`\sin A + \cos A =√(2) \cos A` and we have to prove that

`\cos A - \sin A = √(2) \sin A`.

Now,
`\sin A + \cos A =√(2) \cos A`

⇒
`\sin A = (√(2) - 1 ) \cos A`

⇒
`\sin A = ((2 - 1)* \cos A)/((√(2) + 1 ))`

{By rationalization}

⇒
`(√(2) + 1) \sin A = \cos A`

⇒
`√(2) \sin A + \sin A = \cos A`

⇒
`\cos A - \sin A = √(2) \sin A` (Proved)