Expand (cos(2x))/(sin(x))

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

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

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

Write $\cos (2 x)$ as a fraction with denominator $1$ .

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

Simplify.

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Divide $\cos (2 x)$ by $1$ .

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

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

$\cos (2 x) \csc (x)$

Use the double–angle identity to transform $\cos (2 x)$ to $\cos^{2} (x) - \sin^{2} (x)$ .

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

Apply the distributive property.

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

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

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

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

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

Simplify each term.

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Factor $\cos (x)$ out of $\cos^{2} (x)$ .

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

Separate fractions.

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

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

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

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

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

Expand (cos(2x))/(sin(x))

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