已知tan(π/4+α)=2(1)求tanα的值(2)求(cos2α-sin2α)/(2sinαcosα+cos^2α)的值

Question

已知tan(π/4+α)=2
(1)求tanα的值
(2)求 (cos2α-sin2α)/(2sinαcosα+cos^2α)的值

Answer 1

（1）tan(π/4+α)=(tanπ/4+tanα)/(1-tanπ/4*tanα)=(1+tanα)/(1-tanα)=2
解方程得tanα=1/3
（2）(cos2α-sin2α)/(2sinαcosα+cos^2α)
=(cos^2 α-sin^2 α +2cosαsinα)/(2sinαcosα+cos^2 α)
分子分母同除以cos^2 α
=(1-tan^2 α +2tanα)(2tanα+1)
=(1-1/9+2/3)(2/3 +1)
=14/15
思路就是这样,化成tanα 答案不知道对不对好久没算这种题了