Question

10. (97-7-54) Упростите выражение
$\frac{ \sin(56) \times \sin(124) - \sin(34) \times \cos(236) }{ \cos(28) \times \sin(88) + \sin(178) \times \cos(242) }$
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Answer 1

$\displaystyle\bf\\\frac{Sin56^\circ\cdot Sin124^\circ-Sin34^\circ\cdot Cos236^\circ }{Cos28^\circ\cdot Sin88^\circ+Sin178^\circ\cdot Cos242^\circ}= \\\\\\=\frac{Sin56^\circ\cdot Sin(90^\circ+34^\circ)-Sin34^\circ\cdot Cos(180^\circ+56^\circ) }{Cos28^\circ\cdot Sin(90^\circ-2^\circ) +Sin(180^\circ-2^\circ) \cdot Cos(270^\circ-28^\circ) }=$

$\displaystyle\bf\\=\frac{Sin56^\circ\cdot Cos34^\circ+Sin34^\circ\cdot Cos56^\circ }{Cos28^\circ\cdot Cos2^\circ-Sin2^\circ\cdot Sin28^\circ}=\frac{Sin(56^\circ+34^\circ) }{Cos(28^\circ+2^\circ)} = \\\\\\=\frac{Sin90^\circ}{Cos30^\circ} =\frac{1}{\frac{\sqrt{3} }{2} } =\frac{2}{\sqrt{3} }$