Trigonometry Examples

$\cos (x) (\sec (x) + \csc (x))$

Step 1

Simplify each term.

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Step 1.1

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

$\cos (x) (\frac{1}{\cos (x)} + \csc (x))$

Step 1.2

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

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

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Cancel the common factor of $\cos (x)$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

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

Step 2.3

Combine $\cos (x)$ and $\frac{1}{\sin (x)}$ .

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

Step 3

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

$1 + \cot (x)$