f(x)=(1+cos2x)/[4sin(pai/2+x)]-asin(x/2)cos(pai-x/2)的最大值为2,求a
问题描述:
f(x)=(1+cos2x)/[4sin(pai/2+x)]-asin(x/2)cos(pai-x/2)的最大值为2,求a
答
sin(pai/2+x)=cosxcos(pai-x/2)=-cos(x/2)1+cos2x=1+[2(cosx)^2-1]=2(cosx)^2所以f(x)=2(cosx)^2/4cosx+asin(x/2)cos(x/2)=[(cosx)/2]+[(asinx)/2]=[根号(1+a^2)sin(x+ψ)]/2(其中tanψ=1/a)当sin(x+ψ)=1时,f(x)取...