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Naya [18.7K]
4 years ago
12

="( \sin(x) - \cos(x) ) ^{2} " alt="( \sin(x) - \cos(x) ) ^{2} " align="absmiddle" class="latex-formula">
Mathematics
1 answer:
SIZIF [17.4K]4 years ago
3 0

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)

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