Question

Verify that (sinx- cos x)2 = 1 - 2 sin x cos x is an identity.

Answer 1

Answer:

LHS = RHS

Step-by-step explanation:

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

Since,

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

THEREFORE LHS = RHS