Trigonometry Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

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

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Step 5.1.1

Cancel the common factor.

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

Step 5.1.2

Rewrite the expression.

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

Step 5.2

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

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

Step 6

Multiply the numerator by the reciprocal of the denominator.

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

Step 7

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

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

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

Step 8

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\csc (x)$