Trigonometry Examples

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

Step 1

Apply the distributive property.

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

Step 2

Multiply $\cot (x) \cot (x)$ .

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Add $1$ and $1$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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

Step 4

Rearrange terms.

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

Step 5

Apply pythagorean identity.

$\csc^{2} (x)$