Expand (1-cos(2x))/(1+cos(2x))

$\frac{1 - \cos (2 x)}{1 + \cos (2 x)}$

Simplify the numerator.

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

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

Apply the distributive property.

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

Multiply $- - \sin^{2} (x)$ .

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Multiply $- 1$ by $- 1$ .

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

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

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

Apply pythagorean identity.

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

Add $\sin^{2} (x)$ and $\sin^{2} (x)$ .

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

Simplify the denominator.

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

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

Move $- \sin^{2} (x)$ .

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

Apply pythagorean identity.

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

Add $\cos^{2} (x)$ and $\cos^{2} (x)$ .

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Rewrite the expression.

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

Convert from $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ to $\tan^{2} (x)$ .

$\tan^{2} (x)$

Expand (1-cos(2x))/(1+cos(2x))

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