Trigonometry Examples

$\tan^{2} (2 x) + \cos^{2} (2 x) + \sin^{2} (2 x) = \sec^{2} (2 x)$

Step 1

Start on the left side.

$\tan^{2} (2 x) + \cos^{2} (2 x) + \sin^{2} (2 x)$

Step 2

Apply Pythagorean identity.

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Step 2.1

Rearrange terms.

$\tan^{2} (2 x) + \sin^{2} (2 x) + \cos^{2} (2 x)$

Step 2.2

Apply pythagorean identity.

$\tan^{2} (2 x) + 1$

Step 2.3

Apply pythagorean identity.

$\sec^{2} (2 x)$

Step 3

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

$\tan^{2} (2 x) + \cos^{2} (2 x) + \sin^{2} (2 x) = \sec^{2} (2 x)$ is an identity