∵α∈(π/4,π/2)∴tanα＞1∵tanα＋1/tanα＝5/2＝2＋1/2 ∴tanα＝2∴cos2α＝(1－tan²α)/(1＋tan²α)＝﹣3/5sin2α＝2tanα/(1＋tan²α)＝4/5sin(2α＋π/4)＝√2/2(sin2...