Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = \frac{π}{2} + π n$ , for any integer $n$

Step 3