Trigonometry Examples

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

Step 1

Use the double-angle identity to transform $\cos (2 x)$ to $1 - 2 \sin^{2} (x)$ .

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

Step 2

Apply the sine double-angle identity.

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

Step 3

Multiply $2$ by $- 1$ .

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

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$