Question

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

Answer 1

$(sin x - cos x)^{2} = 1 - 2 sin x cos x$

Step-by-step 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,

$(sin x - cos x)^{2} = 1 - 2 sin x cos x$