Question

упростите выражение:1/(1+ctga)-1/(1-ctga)

Answer 1

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Answer 2

$\frac{1}{1+ctga}-\frac{1}{1-ctga}=\frac{1-ctga-(1+ctga)}{(1+ctga)(1-ctga)}=\frac{-2ctga}{1-ctg^2a}= \frac{2ctga}{ctg^2a-1} =tg2a\\\\\\P.S.\; \; tg2a= \frac{2tga}{1-tg^2a}=\frac{2ctga}{ctg^2a-1}= \frac{2}{ctga-tga}$