Question

数学18题求过程

Answer 1

18、
(1) f(x)=2√3sin(x/2)cos(x/2)+2cos^2(x/2)-1
=√3sinx+cosx
=2sin(x+π/6)
x∈(0,π/2)
x+π/6∈(π/6,2π/3)
当x+π/6=π/2时，f(x)取得最大值：f(x)max=2sinπ/2=2
(2) f(B+C)=2
2sin(B+C+π/6)=2
sin(B+C+π/6)=1
B+C+π/6=π/2
B+C=π/3
A=π-(B+C)
=2π/3
a=√3 b=1

sinB=bsinA/a
=1*sin(2π/3)/√3
=(√3/2)/√3
=1/2
B=π/6
C=π/3-B
=π/6