Precalculus Examples

$\frac{- 8 + 8 \sin (x)}{5 \cos (x)}$

Step 1

Factor $8$ out of $- 8 + 8 \sin (x)$ .

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Step 1.1

Factor $8$ out of $- 8$ .

$\frac{8 \cdot - 1 + 8 \sin (x)}{5 \cos (x)}$

Step 1.2

Factor $8$ out of $8 \cdot - 1 + 8 \sin (x)$ .

$\frac{8 (- 1 + \sin (x))}{5 \cos (x)}$

Step 2

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{8 (- 1 (1) + \sin (x))}{5 \cos (x)}$

Step 3

Factor $- 1$ out of $\sin (x)$ .

$\frac{8 (- 1 (1) - 1 (- \sin (x)))}{5 \cos (x)}$

Step 4

Factor $- 1$ out of $- 1 (1) - 1 (- \sin (x))$ .

$\frac{8 (- 1 (1 - \sin (x)))}{5 \cos (x)}$

Step 5

Move the negative in front of the fraction.

$- \frac{8 (1 - \sin (x))}{5 \cos (x)}$

Step 6

Apply the distributive property.

$- \frac{8 \cdot 1 + 8 (- \sin (x))}{5 \cos (x)}$

Step 7

Multiply $8$ by $1$ .

$- \frac{8 + 8 (- \sin (x))}{5 \cos (x)}$

Step 8

Multiply $- 1$ by $8$ .

$- \frac{8 - 8 \sin (x)}{5 \cos (x)}$

Step 9

Split the fraction $\frac{8 - 8 \sin (x)}{5 \cos (x)}$ into two fractions.

$- (\frac{8}{5 \cos (x)} + \frac{- 8 \sin (x)}{5 \cos (x)})$

Step 10

Separate fractions.

$- (\frac{8}{5} \cdot \frac{1}{\cos (x)} + \frac{- 8 \sin (x)}{5 \cos (x)})$

Step 11

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

$- (\frac{8}{5} \sec (x) + \frac{- 8 \sin (x)}{5 \cos (x)})$

Step 12

Combine $\frac{8}{5}$ and $\sec (x)$ .

$- (\frac{8 \sec (x)}{5} + \frac{- 8 \sin (x)}{5 \cos (x)})$

Step 13

Separate fractions.

$- (\frac{8 \sec (x)}{5} + \frac{- 8}{5} \cdot \frac{\sin (x)}{\cos (x)})$

Step 14

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$- (\frac{8 \sec (x)}{5} + \frac{- 8}{5} \tan (x))$

Step 15

Move the negative in front of the fraction.

$- (\frac{8 \sec (x)}{5} - \frac{8}{5} \tan (x))$

Step 16

Combine $\tan (x)$ and $\frac{8}{5}$ .

$- (\frac{8 \sec (x)}{5} - \frac{\tan (x) \cdot 8}{5})$

Step 17

Move $8$ to the left of $\tan (x)$ .

$- (\frac{8 \sec (x)}{5} - \frac{8 \tan (x)}{5})$