Trigonometry Examples

\sin^{2} (2 x)

$\sin^{2} (2 x)$

Step 1

Apply the sine double-angle identity.

{(2 \sin (x) \cos (x))}^{2}

${(2 \sin (x) \cos (x))}^{2}$

Step 2

Use the power rule

{(a b)}^{n} = a^{n} b^{n}

${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to

2 \sin (x) \cos (x)

$2 \sin (x) \cos (x)$ .

{(2 \sin (x))}^{2} \cos^{2} (x)

${(2 \sin (x))}^{2} \cos^{2} (x)$

Step 2.2

Apply the product rule to

2 \sin (x)

$2 \sin (x)$ .

2^{2} \sin^{2} (x) \cos^{2} (x)

$2^{2} \sin^{2} (x) \cos^{2} (x)$

2^{2} \sin^{2} (x) \cos^{2} (x)

$2^{2} \sin^{2} (x) \cos^{2} (x)$

Step 3

Raise

2

$2$ to the power of

2

$2$ .

4 \sin^{2} (x) \cos^{2} (x)

$4 \sin^{2} (x) \cos^{2} (x)$

\sin^{2} (2 x)

$\sin^{2} (2 x)$

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