Question

Verify that (sinx-cosx)2 = 1 - 2 sin xcosx is an identity.

Answer 1

`(sin x - cos x)^(2) = 1 - 2 sin x cos x`

Explanation:

Step 1 : Taking L.H.S(Left Hand Side) we have,

`(sin x - cos x)^(2) = sin^(2) x + cos^(2) x - 2 sin x cos x` ... equation (1)

Step 2 : As we know,
`sin^(2) x + cos^(2) x = 1`

Therefore,

by substituting value in equation (1), we have

`1 - 2 sin x cos x`

Step 3 : As, L.H.S = R.H.S

Hence Proved,

`(sin x - cos x)^(2) = 1 - 2 sin x cos x`