Trigonometry Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$\frac{\sec (x)}{1} \cdot \frac{1}{\cos (x)}$

Step 6

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\frac{\sec (x)}{1} \sec (x)$

Step 7

Divide $\sec (x)$ by $1$ .

$\sec (x) \sec (x)$

Step 8

Multiply $\sec (x) \sec (x)$ .

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Step 8.1

Raise $\sec (x)$ to the power of $1$ .

$\sec^{1} (x) \sec (x)$

Step 8.2

Raise $\sec (x)$ to the power of $1$ .

$\sec^{1} (x) \sec^{1} (x)$

Step 8.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\sec (x)}^{1 + 1}$

Step 8.4

Add $1$ and $1$ .

$\sec^{2} (x)$