Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

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

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