Question

`( \sin(x) - \cos(x) ) ^(2)`

Answer 1

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)`