f(x)在-π 到π 之間是遞減的
但是f(-3)= -3cos(-3)-sin(-3)=3cos(π-3)+ sin(π-3)>0
f(2)=2cos(2)-sin(2)=-2cos(π-2)-sin(π-2)< 0
∴ f(-3)+f(2) =3cos(π-3)+ sin(π-3)-2cos(π-2)-sin(π-2)
∵cos(π-3)> cos(π-2)>0 ∴cos(π-3)- cos(π-2) >0
cos(π-3)+ sin(π-3) = √2sin(5π/4 - 3)>√2sin(π/4)= 1 > sin(π-2)
即:cos(π-3)+ sin(π-3) > sin(π-2)
∴ f(-3)+f(2) =2[cos(π-3)-cos(π-2) ] +[ cos(π-3)+ sin(π-3)-sin(π-2) ] > 0
f(x)在-π 到π 之間是遞減的
但是f(-3)= -3cos(-3)-sin(-3)=3cos(π-3)+ sin(π-3)>0
f(2)=2cos(2)-sin(2)=-2cos(π-2)-sin(π-2)< 0
∴ f(-3)+f(2) =3cos(π-3)+ sin(π-3)-2cos(π-2)-sin(π-2)
∵cos(π-3)> cos(π-2)>0 ∴cos(π-3)- cos(π-2) >0
cos(π-3)+ sin(π-3) = √2sin(5π/4 - 3)>√2sin(π/4)= 1 > sin(π-2)
即:cos(π-3)+ sin(π-3) > sin(π-2)
∴ f(-3)+f(2) =2[cos(π-3)-cos(π-2) ] +[ cos(π-3)+ sin(π-3)-sin(π-2) ] > 0