Trigonometry Examples

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

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

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

Step 1.2

Factor $\sin (x)$ out of $\sin (x) + \frac{\sin (x)}{\cos (x)}$ .

Tap for more steps...

Step 1.2.1

Multiply by $1$ .

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

Step 1.2.2

Factor $\sin (x)$ out of $\frac{\sin (x)}{\cos (x)}$ .

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

Step 1.2.3

Factor $\sin (x)$ out of $\sin (x) \cdot 1 + \sin (x) \frac{1}{\cos (x)}$ .

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

Step 2

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

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