Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 1096

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\[1)\ 1 + 2\sin a = 2 \bullet \left( \frac{1}{2} + \sin a \right) =\]

\[= 2 \bullet \left( \sin{30{^\circ}} + \sin a \right) =\]

\[= 2 \bullet 2 \bullet \sin\frac{30{^\circ} + a}{2} \bullet\]

\[\bullet \cos\frac{30{^\circ} - a}{2} = 4 \bullet\]

\[\bullet \sin\left( 15{^\circ} + \frac{a}{2} \right) \bullet \cos\left( 15{^\circ} - \frac{a}{2} \right)\]

\[2)\ 1 - 2\sin a = 2 \bullet \left( \frac{1}{2} - \sin a \right) =\]

\[= 2 \bullet \left( \sin{30{^\circ}} - \sin a \right) =\]

\[= 2 \bullet 2 \bullet \sin\frac{30{^\circ} - a}{2} \bullet\]

\[\bullet \cos\frac{30{^\circ} + a}{2} = 4 \bullet\]

\[\bullet \sin\left( 15{^\circ} - \frac{a}{2} \right) \bullet \cos\left( 15{^\circ} + \frac{a}{2} \right)\]

\[3)\ 1 + 2\cos a =\]

\[= 2 \bullet \left( \frac{1}{2} + \cos a \right) = 2 \bullet\]

\[\bullet \left( \cos{60{^\circ}} + \cos a \right) =\]

\[= 2 \bullet 2 \bullet \cos\frac{60{^\circ} + a}{2} \bullet\]

\[\bullet \cos\frac{60{^\circ} - a}{2} = 4 \bullet\]

\[\bullet \cos\left( 30{^\circ} + \frac{a}{2} \right) \bullet \cos\left( 30{^\circ} - \frac{a}{2} \right)\]

\[4)\ 1 + \sin a = \sin{90{^\circ}} + \sin a =\]

\[= 2 \bullet \sin\frac{90{^\circ} + a}{2} \bullet \cos\frac{90{^\circ} - a}{2} =\]

\[= 2 \bullet \sin\left( 45{^\circ} + \frac{a}{2} \right) \bullet\]

\[\bullet \cos\left( 45{^\circ} - \frac{a}{2} \right)\]