Trigonometry Examples

$1 - 2 \sin^{2} (2 x)$

Step 1

Apply the sine double-angle identity.

$1 - 2 {(2 \sin (x) \cos (x))}^{2}$

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

$1 - 2 ({(2 \sin (x))}^{2} \cos^{2} (x))$

Step 2.2

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

$1 - 2 (2^{2} \sin^{2} (x) \cos^{2} (x))$

Step 3

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

$1 - 2 (4 \sin^{2} (x) \cos^{2} (x))$

Step 4

Multiply $4$ by $- 2$ .

$1 - 8 \sin^{2} (x) \cos^{2} (x)$