Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 1081

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\[1)\ \frac{\sin\left( \frac{3\pi}{2} + a \right)}{\text{ctg}(2\pi - a)} \bullet \frac{\text{tg}\left( \frac{\pi}{2} + a \right)}{\sin(\pi + a)} =\]

\[= \frac{- \cos a}{\text{ctg}( - a)} \bullet \frac{- ctg\ a}{- \sin a} =\]

\[= \frac{- \cos a}{- ctg\ a} \bullet \frac{- ctg\ a}{- \sin a} =\]

\[= \frac{\cos a}{\sin a} = ctg\ a\]

\[2)\ \frac{\sin^{2}(\pi + a) + \sin^{2}\left( \frac{\pi}{2} + a \right)}{\cos\left( \frac{3\pi}{2} + a \right)} \bullet\]

\[\bullet \text{ctg}\left( \frac{3\pi}{2} - a \right) =\]

\[= \frac{\left( - \sin a \right)^{2} + \cos^{2}a}{\sin a} \bullet\]

\[\bullet \text{ctg\ }\left( \pi + \frac{\pi}{2} - a \right) =\]

\[= \frac{\sin^{2}a + \cos^{2}a}{\sin a} \bullet ctg\left( \frac{\pi}{2} - a \right) =\]

\[= \frac{1}{\sin a} \bullet tg\ a = \frac{1}{\sin a} \bullet \frac{\sin a}{\cos a} =\]

\[= \frac{1}{\cos a}\]