已知(2sin^2α+sin2α)/(1+tanα)=k,(π/4

题目

已知(2sin^2α+sin2α)/(1+tanα)=k,(π/4

答案

(1) k=[ 2 (sin α)^2 +2 sin α cos α ] / (1 +tan α)=2 sin α (sin α +cos α) / (1 +tan α)=2 sin α cos α (1 +tan α) / (1 +tan α)=sin 2α.因为 π/4< α< π/2,所以 π/2< 2α< π.所以 k=sin 2α ∈...