Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 504

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\[1)\cos a = \frac{4}{5}\]

\[\cos^{2}a = \left( \frac{4}{5} \right)^{2} = \frac{16}{25}\]

\[\sin^{2}a = 1 - \cos^{2}a = \frac{25}{25} - \frac{16}{25} =\]

\[= \frac{9}{25}\]

\[\cos{2a} = \cos^{2}a - \sin^{2}a =\]

\[= \frac{16}{25} - \frac{9}{25} = \frac{7}{25}\]

\[Ответ:\ \ \frac{7}{25}.\]

\[2)\sin a = - \frac{3}{5}\]

\[\sin^{2}a = \left( - \frac{3}{5} \right)^{2} = \frac{9}{25}\]

\[\cos^{2}a = 1 - \sin^{2}a =\]

\[= \frac{25}{25} - \frac{9}{25} = \frac{16}{25}\]

\[\cos{2a} = \cos^{2}a - \sin^{2}a =\]

\[= \frac{16}{25} - \frac{9}{25} = \frac{7}{25}\]

\[Ответ:\ \ \frac{7}{25}.\]