Precalculus Examples

$\frac{\tan (x)}{\sin (x)} + \frac{1}{\cos (x)}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

$\frac{\frac{\sin (x)}{\cos (x)}}{\sin (x)} + \frac{1}{\cos (x)}$

Step 1.2

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

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

Step 1.3

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

Tap for more steps...

Step 1.3.1

Cancel the common factor.

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

Step 1.3.2

Rewrite the expression.

$\frac{1}{\cos (x)} + \frac{1}{\cos (x)}$

Step 2

Combine fractions.

Tap for more steps...

Step 2.1

Combine the numerators over the common denominator.

$\frac{1 + 1}{\cos (x)}$

Step 2.2

Add $1$ and $1$ .

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

Step 3

Separate fractions.

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

Step 4

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

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

Step 5

Divide $2$ by $1$ .

$2 \sec (x)$