Trigonometry Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

$\tan (x) + \frac{\csc (x)}{\sec (x)}$

Step 5

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

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

Step 6

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

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

Step 7

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

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

Step 8

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

$\tan (x) + \cot (x)$