Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 1.2.1

Add parentheses.

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

Step 1.2.2

Rewrite $- \sec (x) \cos (x) (1 - 2 \cos^{2} (x))$ in terms of sines and cosines.

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

Step 1.2.3

Cancel the common factors.

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

Step 1.3

Multiply $- 1$ by $1$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Multiply $- 1$ by $1$ .

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

Step 1.6

Multiply $- 2$ by $- 1$ .

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

Step 2

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

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