若x^2-y^2=1,则1/x^2+2y/x的范围是
问题描述：
若x^2-y^2=1,则1/x^2+2y/x的范围是
用三角换元的方法做,
答
∵x^2-y^2=1,令x=secθ,y=tanθ,θ∈[0,2π],且θ不等于π/2,3π/2,则w=1/(secθ)^2+2tanθ/secθ=-(sinθ-1)^2+2当θ∈[0,π/2)时,w∈[1,2)当θ∈(π,3π/2)时,w∈(-2,1)当θ∈(3π/2,2π]时,w∈(-2,1]∴w的取值范...w=1/(secθ)^2+2tanθ/secθ
=-(sinθ-1)^2+2
这步如何转化而来？w=1/(secθ)^2+2tanθ/secθ
=（cosθ）^2+2tanθ*cosθ
=(cosθ)^2+2sinθ
=1-(sinθ)^2+2sinθ
=-[(sinθ)^2-2sinθ+1-2]
=-[(sinθ-1)^2-2]
=-(sinθ-1)^2+2