Trigonometry Examples

$\sec (x) (\cot (x) + \sin (x))$

Step 1

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

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

Step 2

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

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

Step 3

Simplify terms.

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Step 3.1

Apply the distributive property.

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

Step 3.2

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

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

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

Step 3.3

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

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

Step 4

Simplify each term.

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Step 4.1

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

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

Step 4.2

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

$\csc (x) + \tan (x)$