Respuesta :

Answer:

Simplify: [tex](\sin(x) -\cos(x))^2[/tex]

Use identity rule:

[tex](a-b)^2 = a^2+b^2-2ab[/tex]

Using this rule:

[tex]\sin^2(x)+\cos^2(x)-2\sin(x)\cos(x)[/tex]

Using trigonometric identities rules:

  • [tex]\sin^2(x)+\cos^2(x) = 1[/tex]
  • [tex]2\sin(x)\cos(x) = \sin 2(x)[/tex]

then;

Apply the trigonometric identity rule:

[tex]1-2\sin(x)\cos(x)[/tex]

or

[tex]1-\sin 2(x)[/tex]

Therefore, the simplified form of  [tex](\sin(x) -\cos(x))^2[/tex] is [tex]1-\sin 2(x)[/tex]

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