Question

Найдите значение выражения √72-√288sin²21π/8

Answer 1

так как 288=72*4;
sgrt288=2*sgrt72;
sgrt72 - 2*sgrt72*sin^2(21pi/8)=
=sgrt72(1-2sin^2(21pi/8))=sgrt72*cos(2*21pi/8)=sgrt72*cos21pi/4=
=sgrt72*cos(6pi - 3pi/4)= sgrt72*cos3pi/4= sgrt72*(-sgrt2/2)=- sgrt144/2=  - 12/ 2= - 6