Trigonometry Examples

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

Step 1

Start on the left side.

$\sec^{2} (x)$

Step 2

Convert to sines and cosines.

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Step 2.1

Apply the reciprocal identity to $\sec (x)$ .

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

Step 2.2

Apply the product rule to $\frac{1}{\cos (x)}$ .

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

Step 3

One to any power is one.

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

Step 4

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

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