Trigonometry Examples

$\sec^{2} (θ) = 1 + \tan^{2} (θ)$

Step 1

Start on the right side.

$1 + \tan^{2} (θ)$

Step 2

Apply Pythagorean identity.

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Step 2.1

Rearrange terms.

$\tan^{2} (θ) + 1$

Step 2.2

Apply pythagorean identity.

$\sec^{2} (θ)$

Step 3

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

$\sec^{2} (θ) = 1 + \tan^{2} (θ)$ is an identity