Вычислить sin 11пи/6 * cos 5пи/3 * tg 3пи/4 * ctg 2пи/3. Created by Max150195. matematika-ru

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sin 11пи/6 * cos 5пи/3 * tg 3пи/4 * ctg 2пи/3

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$sin \frac{11 \pi }{6} *cos \frac{5 \pi }{3} *tg \frac{3 \pi }{4} * ctg\frac{2 \pi }{3} = \\ \\ =sin(2 \pi - \frac{ \pi }{6} )*cos (2 \pi -\frac{ \pi }{3} )*tg( \pi - \frac{ \pi }{4} )*ctg( \pi - \frac{ \pi }{3} )= \\ \\ =-sin \frac{ \pi }{6} *cos \frac{ \pi }{3} *(-tg \frac{ \pi }{4} )*(-ctg \frac{ \pi }{3} )= \\ \\ =- \frac{1}{2} * \frac{1}{2} *(-1)*(- \frac{1}{ \sqrt{3} } )=- \frac{1}{4 \sqrt{3} } =- \frac{ \sqrt{3} }{12}$

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