Algebra Examples

$\cot (x) (\frac{1}{\sec (x)} + \frac{1}{\csc (x)})$

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (x)}$ .

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

Step 1.3

Multiply $\cos (x)$ by $1$ .

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

Step 1.4

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

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

Step 1.5

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (x)}$ .

$\cot (x) (\cos (x) + 1 \sin (x))$

Step 1.6

Multiply $\sin (x)$ by $1$ .

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

Step 2

Apply the distributive property.

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

Step 3

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

$\cot (x) \cos (x) + \cos (x)$