Trigonometry Examples

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

Step 1

Rewrite $\csc (x - 1)$ in terms of sines and cosines.

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

Step 2

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

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

Step 3

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

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

Step 4

Rewrite $\csc (x + 1)$ in terms of sines and cosines.

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

Step 5

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

$\sin (x - 1) - (1 \sin (x + 1))$

Step 6

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

$\sin (x - 1) - \sin (x + 1)$