Question

Найдите значение выражения
sqrt(2)-2*sqrt(2)*sin^2(15pi/8)

Answer 1

$sqrt{2} -2 sqrt{2}* sin^2 frac{15 pi }{8} =sqrt{2} -2 sqrt{2} *sin^2(2 pi - frac{ pi }{8} )=$$=sqrt{2} -2 sqrt{2} *sin^2 frac{ pi }{8} =sqrt{2} -2 sqrt{2} * frac{1-cos frac{ pi }{4} }{2} =sqrt{2} - sqrt{2} * ({1- frac{ sqrt{2} }{2} }) =$$=sqrt{2} - sqrt{2} + frac{ sqrt{2} * sqrt{2} }{2} } = frac{2}{2}=1$


P.S.
$sin^2 frac{x}{2} = frac{1-cosx}{2}$

Answer 2

=√2*(1-2*sin² 15π/8)=√2*cos(2*15π/8)=√2*cos(15π/4)=
=√2*cos(4π-π/4)=√2*cos(π/4)=√2*√2/2=2/2=1