Trigonometry Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Write $\cos (x)$ as a fraction with denominator $1$ .

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

Step 5

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

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$\sin (\csc (x) - \sin (x))$