Verify the Identity tan(2x)^2+sin(2x)^2+cos(2x)^2=sec(2x)^2

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

Start on the left side.

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

Apply Pythagorean identity.

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Apply pythagorean identity.

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

Apply pythagorean identity.

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

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

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

Verify the Identity tan(2x)^2+sin(2x)^2+cos(2x)^2=sec(2x)^2

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