Question

求函数Y=根号3COS平方x+二分之一倍sin2x的最大值

Answer 1

Y=√3(Cosx)^2+(1/2)Sin2x

=(√3/2)(1+Cos2x)+(1/2)Sin2x

=√3/2+(√3/2)Cos2x+(1/2)Sin2x

=√3/2+Sin(π/6)Cos2x+Cos(π/6)Sin2x

=√3/2+Sin(π/6+2x)

-1≤Sin(π/6+2x)≤1

√3/2-1≤√3/2+Sin(π/6+2x)≤√3/2+1

√3/2-1≤Y≤√3/2+1

最大值为√3/2+1.