Question

化简：若2α∈(π,2π)，则√{[1-cos(π+2α)]/2}等于？

过程。谢谢。

Answer 1

解：√{[1-cos(π+2α)]/2}
=√[（1+cos2α）/2]
=√[（1+2cos²α-1）/2]
=√cos²α
=│cosα│
∵2α∈(π,2π),∴α∈(π/2,π),∴cosα＜0
∴√{[1-cos(π+2α)]/2}=│cosα│=-cosα

Answer 2

∵2α∈(π,2π)
∴α∈(π/2,π)
∴cosα＜0
∴ √{[1-cos(π+2α)]/2} = √{[1+cos(2α)]/2} =√{[1+2cos^2α-1]/2} =√{cos^2α} = -cosα