Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 1047

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\[1)\ 2\sin{15{^\circ}} \bullet \cos{15{^\circ}} =\]

\[= \sin(2 \bullet 15{^\circ}) = \sin{30{^\circ}} = \frac{1}{2}\]

\[2)\cos^{2}{15{^\circ}} - \sin^{2}{15{^\circ}} =\]

\[= \cos(2 \bullet 15{^\circ}) = \cos{30{^\circ}} = \frac{\sqrt{3}}{2}\]

\[3)\ \frac{2\ tg\ 15{^\circ}}{1 - tg^{2}\ 15{^\circ}} = tg\ (2 \bullet 15{^\circ}) =\]

\[= tg\ 30{^\circ} = \frac{\sqrt{3}}{3}\]

\[4)\ \left( \cos{75{^\circ}} - \sin{75{^\circ}} \right)^{2} =\]

\[= \cos^{2}{75{^\circ}} - 2\cos{75{^\circ}} \bullet \sin{75{^\circ}} +\]

\[+ \sin^{2}{75{^\circ}} =\]

\[= \left( \cos^{2}{75{^\circ}} + \sin^{2}{75{^\circ}} \right) -\]

\[- \sin(2 \bullet 75{^\circ}) = 1 - \sin(150{^\circ}) =\]

\[= 1 - \sin{30{^\circ}} =\]

\[= 1 - \frac{1}{2} = \frac{1}{2}\]