Find the maximum value of (1+cosx)sinx?

Sol
f(x)=(1+Cosx)Sinx=Sinx+Sin2x/2
f’(x)=Cosx+Cos2x
Set f’(x)=0
Cosx+Cos2x=0
Cosx+2Cos^2 x－1=0
2Cos^2x+Cosx－1=0
(2Cosx－1)(Cosx+1)=0
Cosx=1/2 or Cosx=－1
(1) Cosx=1/2
Sinx=+/-√3/2
f(x)=+/-(3/2)*√3/2=+/-3√3/4
(2) Cosx=-1
f(x)=0
So
Max=3√3/4