设f(x)=2cos三次方α+sin²(2π-α)+cos(2π-α)-3/2+2cos²(π+α)+cos(-α),求f(π/3)详细过程

设f(x)=2cos三次方α+sin²(2π-α)+cos(2π-α)-3/2+2cos²(π+α)+cos(-α),求f(π/3)详细过程

f(x)=2cos三次方α+sin²(2π-α)+cos(2π-α)-3/2+2cos²(π+α)+cos(-α),

f(π/3)=2cos^3(π/3)+sin^2(5/3π)+cos5/3π-3/2+2cos^2(4/3π)+cosπ/3
=2(1/2)^3+(-1/2根号3)^2+1/2-3/2+2*(-1/2)^2+1/2
=1/4+3/4+1/2-3/2+2*1/4+1/2
=1-1+1
=1