f(x)=sinx cosx+sinx+cosx+1
設t=sinx+cosx
則t^2=(sinx+cosx)^2=1+2sinx cosx
^2表示平方.
sinx cosx = (t^2-1)/2
f(x)=(t^2-1)/2+t+1
=(t^2)/2+t+1/2
t=sinx+cosx=√2[(√2/2)sinx+(√2/2)cosx]
=√2[sin(x+45度]
所以t的范圍為：[-√2,√2]
f(x)=(t^2)/2+t+1/2的對稱軸為-1
因此當t=-1時取得最小值,1/2-1+1/2=0
當t=√2取得最大值2/2+√2+1/2=3/2+√2