解
x+70=x+10+60
f(x)=3sin(x+10)+5sin(x+10)*cos60+5*sin60*cos(x+10)
=(11/2)sin(x+10)+5*cos(x+10)3^0.5
=7*sin(x+10+α) tanα=(10*3^0.5)/11 辅助角公式
-1≤sin(x+10+α)≤1
f(x)max=7
∴函数f(x)的最大值就是7=11/2*sin(x+10)+5√3/2*cos(x+10)怎么得到的f(x)=3sin(x+10)+5sin(x+10)*cos60+5*sin60*cos(x+10) =3sin(x+10)+5sin(x+10)*1/2+5*√3/2*cos(x+10) 化简合并=(11/2)sin(x+10)+5√3/2*cos(x+10)=7［5.5/7sin(x+10)+5√3/14*cos(x+10)COSα＝5.5/7SINα＝5√3/14=7［sin(x+10)COSα+SINα*cos(x+10)构成二角和三角形函数= 7*sin(x+10+α)