Question

 Помогите вычеслить ответ должен быть: корень2/2

1 - 8 sin^2 17pi/16 cos^2 15pi/16 =

Answer 1

$1 - 8sin^2frac{17pi}{16}cos^2frac{15pi}{16}=1 - 8(sinfrac{17pi}{16}cosfrac{15pi}{16})^2=\ =1-8left(frac{sin(frac{17pi}{16}-frac{15pi}{16})+sin(frac{17pi}{16}+frac{15pi}{16})}2right)^2=1-8left(frac{sinfrac{2pi}{16}+sinfrac{32pi}{16}}2right)^2=\ =1-8left(frac{sinfrac{pi}{8}+sin2pi}2right)^2=1-8left(frac{sinfrac{pi}{8}}2right)^2=1-frac84(sinfracpi8)^2=\ =1-frac84left(sqrt{frac{1-cosfracpi4}2}right)^2=1-2cdotfrac{1-cosfracpi4}2=$

$1-1+cosfracpi4=cosfracpi4=frac{sqrt2}2$