万能代换：设sinx=2k/(1+k^2),cosx=(1-k^2)/(1+k^2).代入得
y=(3k^2+2k+3)/√(5k^2+5+8k+3-3k^2)=(3k^2+2k+3)/√2(k^2+4k+4)=(3k^2+2k+3)/(|k+2|√2)
再令k+2=m代入上式得y=(3m^2-10m+11)/(√2|m|)=(3/√2)(|m|+(11/3)/|m|-10m/(3|m|))
而|m|+(11/3)/|m|-10m/(3|m|)>=2√(11/3)-10/3.这是下界,而上界是正无穷大
所以y的值域是[(3/√2)(2√(11/3)-10/3),正无穷)