Trigonometry Examples

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

Step 1

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

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

Step 2

Apply the distributive property.

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

Step 3

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

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

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

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

Step 5

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

$1 + \cot (x)$