Trigonometry Examples

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

Step 1

Start on the right side.

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

Step 2

Apply the cosine double-angle identity.

$\frac{1}{\cos (2 x)}$

Step 3

Rewrite $\frac{1}{\cos (2 x)}$ as $\sec (2 x)$ .

$\sec (2 x)$

Step 4

Because the two sides have been shown to be equivalent, the equation is an identity.

$\sec (2 x) = \frac{1}{1 - 2 \sin^{2} (x)}$ is an identity