求函数y=1+sinx+cosx+sinxcosx的值域

sinx+cosx=t√2sin(x+∏/4)=t-√2≤t≤√21+2sinxcosx=t²sinxcosx=(t²-1)/2y=1+sinx+cosx+sinxcosx=1+t+(t²-1)/2=t²/2+t+1/2=1/2(t²+2t+1)=1/2(t+1)²t=-1 y=0t=√2 y=1/2(√2+1)²...