Simplify cos(x)-sin(x)tan(x)

$\cos (x) - \sin (x) \tan (x)$

Step 1

Simplify each term.

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

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

Multiply $- \sin (x) \frac{\sin (x)}{\cos (x)}$ .

Combine $\frac{\sin (x)}{\cos (x)}$ and $\sin (x)$ .

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

Raise $\sin (x)$ to the power of $1$ .

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

Raise $\sin (x)$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Step 2

Simplify each term.

Factor $\sin (x)$ out of $\sin^{2} (x)$ .

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

Separate fractions.

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

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

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

Divide $\sin (x)$ by $1$ .

$\cos (x) - \sin (x) \tan (x)$