Question

Вичислите тригонометрическое уравнение 

Answer 1

$8sin^2frac{7pi}{8}cos^2frac{9pi}{8} =8(sinfrac{7pi}{8}cosfrac{9pi}{8})^2=4(sin(frac{7pi}{8}+frac{9pi}{8})+sin(frac{7pi}{8}-frac{9pi}{8}))^2=4(sinfrac{16pi}{8}-sinfrac{2pi}{8})^2=4(sin2pi-sinfrac{pi}{4})^2=4(-frac{sqrt{2}}{2})^2=4cdotfrac{1}{2}=2$