Algebra Examples

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

Step 1

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

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

Step 2

Apply the distributive property.

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

Step 3

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

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

Step 4

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

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

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

$\cot (x) + 1$