Question

化简：根号下1-cosα／1 + cosα在减去根号下1+cosα／1-cosα (3π/2＜α＜

化简：根号下1-cosα／1
+
cosα在减去根号下1+cosα／1-cosα (3π/2＜α＜2π)

Answer 1

∵3π/2＜α＜2π

∴✔｛(1-cosα)／(1+cosα)｝
-｛(1+cosα)／(1-cosα )｝
= ✔｛(1-cosα)²／(1-cos²α)｝-｛(1+cosα)²／(1-cos²α )｝
=(1-cosα)／(-sinα)
-(1+cosα)／(-sinα )
=2/sinα

追答

∵3π/2＜α＜2π

∴✔｛(1-cosα)／(1+cosα)｝
-｛(1+cosα)／(1-cosα )｝
= ✔｛(1-cosα)²／(1-cos²α)｝-｛(1+cosα)²／(1-cos²α )｝
=(1-cosα)／(-sinα)
-(1+cosα)／(-sinα )
=2cosα/sinα
=2cotα