Set 0

Set 0

∵ 0 ＜θ＜π / 2, ∵ - π / 4 ＜θ - π / 4 ＜π / 4, sin θ＞ 0, cos θ＞ 0
From x ^ 2Sin θ - y ^ 2cos θ = 1, x ^ 2 - y ^ 2cot θ = CSC θ,
From x ^ 2cos θ + y ^ 2Sin θ = 1, x ^ 2 + y ^ 2tan θ = sec θ
∴y^2（tanθ＋cotθ）＝secθ－cscθ,
∴y^2（sinθ/cosθ＋cosθ/sinθ）＝1/cosθ－1/sinθ,
∴y^2［（sinθ）^2＋（cosθ）^2］＝sinθ－cosθ,
∴y^2＝sinθ－cosθ＝√2［sinθcos（π/4）－cosθsin（π/4）］＝√2sin（θ－π/4）.
∵ x ^ 2Sin θ - y ^ 2cos θ = 1, x ^ 2cos θ + y ^ 2Sin θ = 1 have four different intersections,
The results show that: y ^ 2 = √ 2Sin (θ - π / 4) > 0, while - π / 4 ＜ θ - π / 4 ＜ π / 4, ‖ 0 ＜θ - π / 4 ＜ π / 4, ‖ π / 4 ＜θ - π / 2
The range of θ satisfying the condition is (π / 4, π / 2)