Trigonometry Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

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

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

Step 4

Simplify.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Add $1$ and $1$ .

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

Step 5

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

$\sec (x) \sin^{2} (x)$

Step 6

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

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

Step 7

Combine $\frac{1}{\cos (x)}$ and $\sin^{2} (x)$ .

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

Step 8

Factor $\sin (x)$ out of $\sin^{2} (x)$ .

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

Step 9

Separate fractions.

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

Step 10

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

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

Step 11

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

$\sin (x) \tan (x)$