Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 1128

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\[1)\sin{35{^\circ}} + \sin{25{^\circ}} = \cos{5{^\circ}}\]

\[2 \bullet \sin\frac{35{^\circ} + 25{^\circ}}{2} \bullet\]

\[\bullet \cos\frac{35{^\circ} - 25{^\circ}}{2} = \cos{5{^\circ}}\]

\[2 \bullet \sin\frac{60{^\circ}}{2} \bullet \cos\frac{10{^\circ}}{2} = \cos{5{^\circ}}\]

\[2 \bullet \sin{30{^\circ}} \bullet \cos{5{^\circ}} = \cos{5{^\circ}}\]

\[2 \bullet \frac{1}{2} \bullet \cos{5{^\circ}} = \cos{5{^\circ}}\]

\[\cos{5{^\circ}} = \cos{5{^\circ}}\]

\[Что\ и\ требовалось\ доказать.\]

\[2)\cos{12{^\circ}} - \cos{48{^\circ}} = \sin{18{^\circ}}\]

\[- 2 \bullet \sin\frac{12{^\circ} + 48{^\circ}}{2} \bullet\]

\[\bullet \sin\frac{12{^\circ} - 48{^\circ}}{2} = \sin{18{^\circ}}\]

\[- 2 \bullet \sin\frac{60{^\circ}}{2} \bullet \sin\left( - \frac{36{^\circ}}{2} \right) =\]

\[= \sin{18{^\circ}}\]

\[2 \bullet \sin{30{^\circ}} \bullet \sin{18{^\circ}} = \sin{18{^\circ}}\]

\[2 \bullet \frac{1}{2} \bullet \sin{18{^\circ}} = \sin{18{^\circ}}\]

\[\sin{18{^\circ}} = \sin{18{^\circ}}\]

\[Что\ и\ требовалось\ доказать.\]