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

asked Nov 17, 2021 41.7k views

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5 votes

Answer:

LHS = RHS

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

Giaset answered Nov 23, 2021

4.0k points

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