Trigonometry Examples

$\sin (x) \tan (\frac{x}{2})$

Step 1

Rewrite $\tan (\frac{x}{2})$ in terms of sines and cosines.

$\sin (x) \frac{\sin (\frac{x}{2})}{\cos (\frac{x}{2})}$

Step 2

Combine $\sin (x)$ and $\frac{\sin (\frac{x}{2})}{\cos (\frac{x}{2})}$ .

$\frac{\sin (x) \sin (\frac{x}{2})}{\cos (\frac{x}{2})}$

Step 3

Separate fractions.

$\frac{\sin (\frac{x}{2})}{1} \cdot \frac{\sin (x)}{\cos (\frac{x}{2})}$

Step 4

Rewrite $\frac{\sin (x)}{\cos (\frac{x}{2})}$ as a product.

$\frac{\sin (\frac{x}{2})}{1} (\sin (x) \frac{1}{\cos (\frac{x}{2})})$

Step 5

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

$\frac{\sin (\frac{x}{2})}{1} (\frac{\sin (x)}{1} \cdot \frac{1}{\cos (\frac{x}{2})})$

Step 6

Simplify.

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Step 6.1

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

$\frac{\sin (\frac{x}{2})}{1} (\sin (x) \frac{1}{\cos (\frac{x}{2})})$

Step 6.2

Convert from $\frac{1}{\cos (\frac{x}{2})}$ to $\sec (\frac{x}{2})$ .

$\frac{\sin (\frac{x}{2})}{1} (\sin (x) \sec (\frac{x}{2}))$

Step 7

Divide $\sin (\frac{x}{2})$ by $1$ .

$\sin (\frac{x}{2}) \sin (x) \sec (\frac{x}{2})$