Trigonometry Examples

$\frac{\sec (x) \sin (x)}{\tan (x) \cot (x)}$

Step 1

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

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Combine fractions.

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Step 3.1

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

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

Step 3.2

Multiply $\frac{\sin (x)}{\cos (x)}$ by $\frac{\cos (x)}{\sin (x)}$ .

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

Step 4

Simplify the denominator.

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Step 4.1

Reduce the expression $\frac{\sin (x) \cos (x)}{\cos (x) \sin (x)}$ by cancelling the common factors.

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Step 4.1.1

Cancel the common factor.

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

Step 4.1.2

Rewrite the expression.

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

Step 4.2

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

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Step 4.2.1

Cancel the common factor.

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

Step 4.2.2

Rewrite the expression.

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

Step 5

Divide $\frac{\sin (x)}{\cos (x)}$ by $1$ .

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

Step 6

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

$\tan (x)$