答
tana+cota=-10/3
3tan^2a+10tana+3=0
(3tana+1)(1+3tana)=0
tana=-1/3,或tana=-3
因为3π/4所以,
tana=-1/3
(5sin²a/2+8sina/2cosa/2+11cos²a/2-8)/√2sin(a-π/4)
=[5(1-cosa)/2+4sina+11(1+cosa)/2-8]/(sina-cosa)
=(3cosa+4sina)/(sina-cosa)
=(3+4tana)/(tana-1)
=(3-4/3)/(-1/3-1)
=(5/3) / (-4/3)
=-5/4
