1.[sin50°（1+根号3倍tan10°）-cos20°]/[cos80°根号下1-cos20°]
={2sin50°[(1/2)cos10°+(√3/2)sin10°]/cos10°-cos20°}/[sin10°√2*√(sin10°)^2]
=[(2cos40°sin40°)/cos10°-cos20°]/[√2sin10°*sin10°]
=(sin80°/sin80°-cos20°)/[√2(sin10°)^2]
=(1-cos20°)/[√2(sin10°)^2]
=2(sin10°)^2/[√2(sin10°)^2]
=√2
2.6sin²α+sinαcosα-2cos²α=0
(3sinα+2cosα)(2sinα-cosα)=0
∵α∈（π/2,π)
∴sinα>0 cosα0
∴3sinα+2cosα=0
3sinα=-2cosα
平方9sin²α=4cos²α=4-4sin²α
解得sinα=2/√13 cosα=-3/√13
sin2α=2sinαcosα=-12/13 cos2α=1-2sin²α=5/13
所以sin(2α+π/3)=sin2αcos(π/3)+cos2αsin(π/3)
=(-12/13)*(1/2)+(5/13)*(√3/2)
=(5√3-12)/26
3.cos2α=2cos²α-1=7/25
cos²α=16/25
cosα=±4/5
sin(α-π/4)=sinαcos(π/4)-cosαsin(π/4)=7√2/10
cosα=4/5时 (√2/2)sinα=7√2/10+(√2/2)*(4/5)
sinα=7/5+4/5>1不成立
所以cosα=-4/5
(√2/2)sinα=7√2/10+(√2/2)(-4/5)
解得sinα=3/5
tanα=sinα/cosα=-3/4
所以tan(a+π/3)=[tana+tan(π/3)]/[1-tanatan(π/3)]
=(-3/4+√3)/[1-√3(-3/4)]
=(25√3-48)/11