Trigonometry Examples

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

Step 1

Apply pythagorean identity.

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

Step 2

Rewrite $\frac{\tan^{2} (x)}{\sec^{2} (x)}$ as ${(\frac{\tan (x)}{\sec (x)})}^{2}$ .

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

Step 3

Rewrite $\sec (x)$ in terms of sines and cosines.

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

Step 4

Rewrite $\tan (x)$ in terms of sines and cosines.

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

Step 5

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (x)}$ .

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

Step 6

Write $\cos (x)$ as a fraction with denominator $1$ .

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

Step 7

Cancel the common factor of $\cos (x)$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

$\sin^{2} (x)$