Trigonometry Examples

$\sin^{2} (2 a) + \cos^{2} (a)$

Step 1

Apply the sine double-angle identity.

${(2 \sin (a) \cos (a))}^{2} + \cos^{2} (a)$

Step 2

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

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Step 2.1

Apply the product rule to $2 \sin (a) \cos (a)$ .

${(2 \sin (a))}^{2} \cos^{2} (a) + \cos^{2} (a)$

Step 2.2

Apply the product rule to $2 \sin (a)$ .

$2^{2} \sin^{2} (a) \cos^{2} (a) + \cos^{2} (a)$

Step 3

Raise $2$ to the power of $2$ .

$4 \sin^{2} (a) \cos^{2} (a) + \cos^{2} (a)$