Trigonometry Examples

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

Step 1

Simplify the denominator.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

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

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