tan(a+π/4)=2,则1+3sina*cosa-2*cosa^2=?
问题描述：
tan(a+π/4)=2,则1+3sina*cosa-2*cosa^2=?
答
tan(a+π/4)=2 = [1 + tana]/[1 - tana] ,解得tana = 1/3
1+3sina*cosa-2*cosa^2 = (3/2)·sin(2a) - cos(2a)
sin(2a) = 2tana/[1 + (tana)^2] = 3/5
cos(2a) = [1 - (tana)^2]/[1 + (tana)^2] = 4/5
故：1+3sina*cosa-2*cosa^2 = (3/2)·（3/5） - 4/5 = 1/10