已知tanθ=a(a>1),求sin(π/4+θ)/sin(π/2-θ)×tan2θ的值

题目

已知tanθ=a(a>1),求sin(π/4+θ)/sin(π/2-θ)×tan2θ的值

答案

sin(π/4+θ)/sin(π/2-θ)×tan2θ
=sin(π/4+θ)/cos(θ)×(2tanθ)/[1-(tanθ)^2]
=√2/2*(tanθ+1))×(2tanθ)/[1-(tanθ)^2]
=√2/2*(a+1)*[2a/(1-a^2)]
=√2*a/(1-a)