Trigonometry Examples

$\tan^{3} (x) - \tan (x) \sec^{2} (x)$

Step 1

Factor $\tan (x)$ out of $\tan^{3} (x) - \tan (x) \sec^{2} (x)$ .

Tap for more steps...

Step 1.1

Factor $\tan (x)$ out of $\tan^{3} (x)$ .

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

Step 1.2

Factor $\tan (x)$ out of $- \tan (x) \sec^{2} (x)$ .

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

Step 1.3

Factor $\tan (x)$ out of $\tan (x) \tan^{2} (x) + \tan (x) (- 1 \sec^{2} (x))$ .

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

Step 2

Reorder $\tan^{2} (x)$ and $- 1 \sec^{2} (x)$ .

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

Step 3

Factor $- 1$ out of $- 1 \sec^{2} (x)$ .

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

Step 4

Factor $- 1$ out of $\tan^{2} (x)$ .

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

Step 5

Factor $- 1$ out of $- 1 (\sec^{2} (x)) - 1 (- \tan^{2} (x))$ .

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

Step 6

Factor.

Tap for more steps...

Step 6.1

Apply pythagorean identity.

$\tan (x) (- 1 \cdot 1)$

Step 6.2

Remove unnecessary parentheses.

$\tan (x) \cdot - 1 \cdot 1$

Step 7

Combine exponents.

Tap for more steps...

Step 7.1

Factor out negative.

$- (\tan (x) \cdot 1)$

Step 7.2

Multiply $\tan (x)$ by $1$ .

$- \tan (x)$