Trigonometry Examples

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

Step 1

Rewrite $\frac{\sin (x + y)}{\sin (x - y)}$ as a product.

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

Step 2

Write $\sin (x + y)$ as a fraction with denominator $1$ .

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

Step 3

Simplify.

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Step 3.1

Divide $\sin (x + y)$ by $1$ .

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

Step 3.2

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

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