Question

78 баллов!
$sin(x+\pi/3)+sin(x-\pi/3)$ , если sin(x) = $\sqrt{3} /4$
Очень срочно

Answer 1

$sin x = \sqrt{3} /4 \\cosx^{2} = 1- sinx^{2} =1- \frac{3}{16} =\frac{13}{16} \\sin(x+\pi /3) = sinx * sin60 + cosx*cos60= \sqrt{3}/4*\sqrt{3} /2 + \sqrt{13} /4*1/2=3/8+\sqrt{13} /8=\frac{3+\sqrt{13} }{8} \\\\sin(x-\pi /3)=sinx * sin60 - cosx*cos60 = \sqrt{3}/4*\sqrt{3} /2 - \sqrt{13} /4*1/2=3/8-\sqrt{13} /8=\frac{3-\sqrt{13} }{8} \\\\sin(x+\pi /3) + sin(x-\pi /3) = \frac{3+\sqrt{13} }{8} + \frac{3-\sqrt{13} }{8} =\frac{6}{8}$

ответ 6/8