Trigonometry Examples

$\cot (x) - 2 \cos (x) \cot (x)$

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Multiply $- 2 \cos (x) \frac{\cos (x)}{\sin (x)}$ .

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Step 1.3.1

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

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

Step 1.3.2

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

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

Step 1.3.3

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

$\frac{\cos (x)}{\sin (x)} + \frac{- 2 (\cos^{1} (x) \cos (x))}{\sin (x)}$

Step 1.3.4

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

$\frac{\cos (x)}{\sin (x)} + \frac{- 2 (\cos^{1} (x) \cos^{1} (x))}{\sin (x)}$

Step 1.3.5

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

$\frac{\cos (x)}{\sin (x)} + \frac{- 2 {\cos (x)}^{1 + 1}}{\sin (x)}$

Step 1.3.6

Add $1$ and $1$ .

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

Step 1.4

Move the negative in front of the fraction.

$\frac{\cos (x)}{\sin (x)} - \frac{2 \cos^{2} (x)}{\sin (x)}$

Step 2

Simplify each term.

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Step 2.1

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

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

Step 2.2

Factor $\cos (x)$ out of $\cos^{2} (x)$ .

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

Step 2.3

Separate fractions.

$\cot (x) - (\frac{2 (\cos (x))}{1} \cdot \frac{\cos (x)}{\sin (x)})$

Step 2.4

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

$\cot (x) - (\frac{2 (\cos (x))}{1} \cot (x))$

Step 2.5

Divide $2 (\cos (x))$ by $1$ .

$\cot (x) - (2 (\cos (x)) \cot (x))$

Step 2.6

Multiply $2$ by $- 1$ .

$\cot (x) - 2 \cos (x) \cot (x)$