化简√(1+sinθ）-√（1-sinθ）

Question

化简√(1+sinθ）-√（1-sinθ）

Answer 1

√(1+sinθ)-√(1-sinθ)
=√[1+2sin(θ/2)cos(θ/2)]-√[1-2sin(θ/2)cos(θ/2)]
=√[sin²(θ/2)+2sin(θ/2)cos(θ/2)+cos²(θ/2)]-√[sin²(θ/2)-2sin(θ/2)cos(θ/2)+cos²(θ/2)]
=√[sin(θ/2)+cos(θ/2)]²-√[sin(θ/2)-cos(θ/2)]²
=|sin(θ/2)+cos(θ/2)|+|sin(θ/2)-cos(θ/2)|
有没有给出θ的范围?有的话上面可以继续化简下去.