Question

="( \sin(x) - \cos(x) ) ^{2} " alt="( \sin(x) - \cos(x) ) ^{2} " align="absmiddle" class="latex-formula">

Answer 1

Answer:

Simplify: $(\sin(x) -\cos(x))^2$

Use identity rule:

$(a-b)^2 = a^2+b^2-2ab$

Using this rule:

$\sin^2(x)+\cos^2(x)-2\sin(x)\cos(x)$

Using trigonometric identities rules:

• $\sin^2(x)+\cos^2(x) = 1$

• $2\sin(x)\cos(x) = \sin 2(x)$

then;

Apply the trigonometric identity rule:

$1-2\sin(x)\cos(x)$

or

$1-\sin 2(x)$

Therefore, the simplified form of  $(\sin(x) -\cos(x))^2$ is $1-\sin 2(x)$