Упростите: sin^2x/(1-cosx)-cosx С объяснением.. Created by Gothic22. algebra-ru

(1-cosx)-cosx С объяснением...

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Применим основное тригонометрическое тождество и формулу разности квадратов:
$\dfrac{sin^2x}{1 - cosx} - cosx = \dfrac{1 - cos^2x}{1 - cosx} - cosx = \\ \\ 
 \dfrac{(1 - cosx)(1 + cosx)}{1 - cosx} - cosx = 1 + cosx - cosx = 1$

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

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