30 БАЛЛОВ РЕШИТЕ ЗАДАЧИ (cosa/1+sina+cos/1-sina)*sin2a tg(p-a)/cos(p+a)*sin 3p/2+a/ctg(3p/2-a). Created by jsiskwnedjxin. algebra-ru

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30 БАЛЛОВ
РЕШИТЕ ЗАДАЧИ

(cosa/1+sina+cos/1-sina)*sin2a

tg(p-a)/cos(p+a)*sin 3p/2+a/ctg(3p/2-a)

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Ответ:

$1)\ \ \Big(\dfrac{cosa}{1+sina}+\dfrac{cosa}{1-sina}\Big)\cdot sin2a=\dfrac{cosa(1-sina)+cosa(1+sina)}{(1+sina)(1-sina)}\cdot sin2a=\\\\\\=\dfrac{2\, cosa}{1-sin^2a}\cdot sin2a=\dfrac{2\, cosa}{cos^2a}\cdot 2\, sina\cdot cosa=4\, sina$

$2)\ \ \dfrac{tg(\pi -a)}{cos(\pi+a)}\cdot \dfrac{sin(\frac{3\pi}{2}+a)}{ctg(\frac{3\pi }{2}-a)}=\dfrac{-tga}{-cosa}\cdot \dfrac{-cosa}{tga}=-1$

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