Question

求大神啊！！！要详解！！！谢谢，快

Answer 1

(1)m^2=4[cos(x/2)]^2+1=2(1+cosx)+2=3+2cosx,
mn=2cos(x/2)[-sin(x/2)]+3cosx=-sinx+3cosx,
∴f(x)=(m-n)m=m^2-mn=3+sinx-cosx=3+√2sin(x-π/4),
其最大值=3+√2，
对任意x∈R,f(x)<=a,
<==>a>=3+√2，为所求.
(2)f(A)=3+√2sin(A-π/4)=4,sin(A-π/4)=√2/2，A-π/4=π/4，A=π/2，
a=√10，b=√10sinB,c=√10cosB,
∴S=(1/2)bc=5sin2B<=5,当B=π/4时取等号，
∴S的最大值是5.