设f(x)=[2cos^3 x-sin^2 (360°-x)+2sin(90°+x)+1]/2+2cos^2 (180°+x)+cos(-x),求f(π/3)的值

题目

设f(x)=[2cos^3 x-sin^2 (360°-x)+2sin(90°+x)+1]/2+2cos^2 (180°+x)+cos(-x),求f(π/3)的值
设f(x)=[2cos^3 x-sin^2 (360°-x)+2sin(90°+x)+1]/2+2cos^2 (180°+x)+cos(-x),求f(π/3)的值

答案

f(x)=[2cos³x+sin²(-x)+2cosx+1]/[2+2(-cosx)²+cosx]=(2cos³x+sin²x+2cosx+1)/[2+2cos²x+cosx]cosπ/3=1/2,sinπ/3=√3/2f(π/3)=(1/4+3/4+1+1)/(2+1/2+1/2)=1