Trigonometry Examples

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

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

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

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

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

Rewrite $\frac{\frac{\sin (x)}{\cos (x)}}{\sin (x)}$ as a product.

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

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

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Cancel the common factor.

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

Rewrite the expression.

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

Simplify the expression.

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

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

One to any power is one.

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

Rewrite $1$ as $1^{2}$ .

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

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

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

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\sec^{2} (x)$