Trigonometry Examples

$\sin (q) + \cos (q) \cot (q)$

Step 1

Simplify each term.

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Step 1.1

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

$\sin (q) + \cos (q) \frac{\cos (q)}{\sin (q)}$

Step 1.2

Multiply $\cos (q) \frac{\cos (q)}{\sin (q)}$ .

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Step 1.2.1

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

$\sin (q) + \frac{\cos (q) \cos (q)}{\sin (q)}$

Step 1.2.2

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

$\sin (q) + \frac{\cos^{1} (q) \cos (q)}{\sin (q)}$

Step 1.2.3

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

$\sin (q) + \frac{\cos^{1} (q) \cos^{1} (q)}{\sin (q)}$

Step 1.2.4

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

$\sin (q) + \frac{{\cos (q)}^{1 + 1}}{\sin (q)}$

Step 1.2.5

Add $1$ and $1$ .

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

Step 2

Simplify each term.

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Step 2.1

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

$\sin (q) + \frac{\cos (q) \cos (q)}{\sin (q)}$

Step 2.2

Separate fractions.

$\sin (q) + \frac{\cos (q)}{1} \cdot \frac{\cos (q)}{\sin (q)}$

Step 2.3

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

$\sin (q) + \frac{\cos (q)}{1} \cot (q)$

Step 2.4

Divide $\cos (q)$ by $1$ .

$\sin (q) + \cos (q) \cot (q)$