展开-(sec^2(x/2))/((tan(x/2)-1)^2)

解答

展开

- \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} )}

求解步骤

- \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}

化简

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} )}

e x p an d - \frac{1}{8} (36 x - 16 y)

e x p an d \frac{x ^{2} - 9}{x ( x ^{2} + 1 )}

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