Question

Вичислите тригонометрическое уравнение

Answer 1

$8sin^2\frac{7\pi}{8}cos^2\frac{9\pi}{8} =8(sin\frac{7\pi}{8}cos\frac{9\pi}{8})^2=4(sin(\frac{7\pi}{8}+\frac{9\pi}{8})+sin(\frac{7\pi}{8}-\frac{9\pi}{8}))^2=4(sin\frac{16\pi}{8}-sin\frac{2\pi}{8})^2=4(sin2\pi-sin\frac{\pi}{4})^2=4(-\frac{\sqrt{2}}{2})^2=4\cdot\frac{1}{2}=2$