Trigonometry Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify.

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Step 3.1

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

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

Step 3.2

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

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

Step 4

Use the double-angle identity to transform $\cos (2 x)$ to $2 \cos^{2} (x) - 1$ .

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

Step 5

Apply the distributive property.

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

Step 6

Rewrite $- 1 \csc (x)$ as $- \csc (x)$ .

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