Trigonometry Examples

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

Step 1

Start on the right side.

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

Step 2

Convert to sines and cosines.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Simplify.

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Step 3.1

One to any power is one.

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

Step 3.2

Cancel the common factor of ${\cos (x)}^{2}$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

$1$

Step 4

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

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