若F(X)=cos∧2(x/4)-2sin∧2(x/4)+3√3sin(x/4)*cos(x/4) x∈(2/3派,3/4派),求f(X)的最大值
问题描述:
若F(X)=cos∧2(x/4)-2sin∧2(x/4)+3√3sin(x/4)*cos(x/4) x∈(2/3派,3/4派),求f(X)的最大值
答
f(x)=cos(x/2)-sin^2(x/4)+3根号3/2sin(x/2)
=cos(x/2)-(1-cos(x/2))/2+3根号3/2sinx/2
=3/2cosx/2+3根号3/2sinx/2-1/2
=3sin(x/2+Pai/6)-1/2
2/3Pai=