Question

Найдите значение выражения√32 cos^2 5П/8 - √8

Answer 1

√32 cos² 5π/8 - √8=4√2*cos² 5π/8-2√2=2√2*(2cos² 5π/8-1)=

2√2*(1+cos10π/8-1)=2√2*cos5π/4=2√2*cos5π/4=

2√2*cos(π+π/4)=-2√2*cosπ/4=-2√2*√2/2= -2