Trigonometry Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

$\cot (t) (\tan (t) \sec^{2} (t) + \tan (t) (- \tan^{2} (t)))$

Step 1.3

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

$\cot (t) (\tan (t) (\sec^{2} (t) - \tan^{2} (t)))$

Step 2

Apply pythagorean identity.

$\cot (t) (\tan (t) \cdot 1)$

Step 3

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

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Step 3.1

Rewrite $\cot (t) (\tan (t) \cdot 1)$ in terms of sines and cosines.

$\frac{\cos (t)}{\sin (t)} \cdot \frac{\sin (t)}{\cos (t)} \cdot 1$

Step 3.2

Cancel the common factors.

$1 \cdot 1$

Step 4

Multiply $1$ by $1$ .

$1$