Trigonometry Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

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

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

Step 4

Simplify.

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Step 4.1

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

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

Step 4.2

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

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

Step 5

Convert from $\frac{1}{\cos (y)}$ to $\sec (y)$ .

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