Trigonometry Examples

$\frac{\sin (2 x)}{2 \csc (x)} - \cos^{3} (x)$

Step 1

Separate fractions.

$\frac{1}{2} \cdot \frac{\sin (2 x)}{\csc (x)} - \cos^{3} (x)$

Step 2

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

$\frac{1}{2} \cdot \frac{\sin (2 x)}{\frac{1}{\sin (x)}} - \cos^{3} (x)$

Step 3

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

$\frac{1}{2} (\sin (2 x) \sin (x)) - \cos^{3} (x)$

Step 4

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

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Step 4.1

Combine $\sin (2 x)$ and $\frac{1}{2}$ .

$\frac{\sin (2 x)}{2} \sin (x) - \cos^{3} (x)$

Step 4.2

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

$\frac{\sin (2 x) \sin (x)}{2} - \cos^{3} (x)$