Algebra Examples

$\sqrt{\frac{\cot^{2} (x) + 1}{\tan^{2} (x) + 1}}$

Step 1

Rearrange terms.

$\sqrt{\frac{1 + \cot^{2} (x)}{\tan^{2} (x) + 1}}$

Step 2

Apply pythagorean identity.

$\sqrt{\frac{\csc^{2} (x)}{\tan^{2} (x) + 1}}$

Step 3

Apply pythagorean identity.

$\sqrt{\frac{\csc^{2} (x)}{\sec^{2} (x)}}$

Step 4

Rewrite $\frac{\csc^{2} (x)}{\sec^{2} (x)}$ as ${(\frac{\csc (x)}{\sec (x)})}^{2}$ .

$\sqrt{{(\frac{\csc (x)}{\sec (x)})}^{2}}$

Step 5

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

$\sqrt{{(\frac{\csc (x)}{\frac{1}{\cos (x)}})}^{2}}$

Step 6

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

$\sqrt{{(\frac{\frac{1}{\sin (x)}}{\frac{1}{\cos (x)}})}^{2}}$

Step 7

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

$\sqrt{{(\frac{\cos (x)}{\sin (x)})}^{2}}$

Step 8

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

$\sqrt{\cot^{2} (x)}$

Step 9

Pull terms out from under the radical, assuming positive real numbers.

$\cot (x)$