Trigonometry Examples

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

Step 1

Simplify with factoring out.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.1.3

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 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

Apply pythagorean identity.

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

Step 3

Simplify the expression.

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Step 3.1

Multiply $- 1$ by $1$ .

$\tan (x) \cdot - 1$

Step 3.2

Move $- 1$ to the left of $\tan (x)$ .

$- 1 \cdot \tan (x)$

Step 3.3

Rewrite $- 1 \tan (x)$ as $- \tan (x)$ .

$- \tan (x)$