Trigonometry Examples

$\tan (x) (\tan (x) + \cot (x))$

Step 1

Apply the distributive property.

$\tan (x) \tan (x) + \tan (x) \cot (x)$

Step 2

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

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Step 2.1

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

$\tan^{1} (x) \tan (x) + \tan (x) \cot (x)$

Step 2.2

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

$\tan^{1} (x) \tan^{1} (x) + \tan (x) \cot (x)$

Step 2.3

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

${\tan (x)}^{1 + 1} + \tan (x) \cot (x)$

Step 2.4

Add $1$ and $1$ .

$\tan^{2} (x) + \tan (x) \cot (x)$

Step 3

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

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Step 3.1

Reorder $\tan (x)$ and $\cot (x)$ .

$\tan^{2} (x) + \cot (x) \tan (x)$

Step 3.2

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

$\tan^{2} (x) + \frac{\cos (x)}{\sin (x)} \cdot \frac{\sin (x)}{\cos (x)}$

Step 3.3

Cancel the common factors.

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

Step 4

Apply pythagorean identity.

$\sec^{2} (x)$