1.∵a⊥b
∴a*b=0
∴3sinα*2sinα+5sinαcosα-4cos²α=0
∴6tan²α+5tanα-4=0
(2tanα-1)(3tanα+4)=0
tanα=1/2或-4/3
∵α∈(3π/2,2π)
∴tanα=-4/3
2.∵tanα=-4/3
∴sinα=4/5 cosα=-3/5
∴cos(α/2+π/3)=1/2cosα/2-√3/2sinα/2
=1/2√[(cosα+1)/2]-√3/2*sinα/(2cosα/2)
=1/2*√5/5-√3/2*4/5/(2√5/5)
=√5/10-√15/5
=(√5-2√15)/10