What is expand-(sec^2(x/2))/((tan(x/2)-1)^2) ?

The solution to expand-(sec^2(x/2))/((tan(x/2)-1)^2) is -(sec^2(x/2))/(-2tan(x/2)+sec^2(x/2))

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expand-(sec^2(x/2))/((tan(x/2)-1)^2)

expand

- \frac{sec ^{2} ( \frac{x}{2} )}{( tan ( \frac{x}{2} ) - 1 ) ^{2}}

- \frac{sec ^{2} ( \frac{x}{2} )}{- 2 tan ( \frac{x}{2} ) + sec ^{2} ( \frac{x}{2} )}

Solution steps

- \frac{sec ^{2} ( \frac{x}{2} )}{( tan ( \frac{x}{2} ) - 1 ) ^{2}}

(tan (\frac{x}{2}) - 1)^{2} = tan^{2} (\frac{x}{2}) - 2 tan (\frac{x}{2}) + 1

= - \frac{sec ^{2} ( \frac{x}{2} )}{tan ^{2} ( \frac{x}{2} ) - 2 tan ( \frac{x}{2} ) + 1}

Simplify

tan^{2} (\frac{x}{2}) - 2 tan (\frac{x}{2}) + 1 : sec^{2} (\frac{x}{2}) - 2 tan (\frac{x}{2})

= - \frac{sec ^{2} ( \frac{x}{2} )}{sec ^{2} ( \frac{x}{2} ) - 2 tan ( \frac{x}{2} )}

- \frac{1}{8} (36 x - 16 y)

x \cdot (1 - x - y) \cdot e^{y}

\frac{x ^{2} - 9}{x ( x ^{2} + 1 )}

(z^{2} (a) + z (b) + c) \cdot (z^{2} (d) + z (e) + f)

(x + \frac{10}{3}) (x + 10)

What is expand-(sec^2(x/2))/((tan(x/2)-1)^2) ?
The solution to expand-(sec^2(x/2))/((tan(x/2)-1)^2) is -(sec^2(x/2))/(-2tan(x/2)+sec^2(x/2))