Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Combine $2$ and $\frac{\cos (x)}{\sin (x)}$ .

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

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Add $2 \cos (x)$ and $\cos (x)$ .

$\frac{3 \cos (x)}{\sin (x)}$

Step 3

Separate fractions.

$\frac{3}{1} \cdot \frac{\cos (x)}{\sin (x)}$

Step 4

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

$\frac{3}{1} \cot (x)$

Step 5

Divide $3$ by $1$ .

$3 \cot (x)$