已知sinαsinβ=1/2,求cosαsinβ的范围.

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已知sinαsinβ=1/2,求cosαsinβ的范围.

已知sinαsinβ=1/2,求cosαsinβ的范围.
已知sinαsinβ=1/2,求cosαsinβ的范围.

已知sinαsinβ=1/2,求cosαsinβ的范围.
sina=1/2sinb
(sina)^2=1/4(sinb)^2
(cosa)^2=1-(sina)^2=1-1/4(sinb)^2=[4(sinb)^2-1]/[4(sinb)^2]
(cosa)^2(sinb)^2=[4(sinb)^2-1]/4=(sinb)^2-1/4
0

faaef=12312.

sinβ=1/(2sinα)
-1<=sinβ<=1
=>
-2<=1/sinα<=2
=>
1/2<=sinα<=1
或-1<=sinα<=-1/2
不妨设α在[0,2pai)
=>
pai/6<=α<=5pai/6

7pai/6<=α<=11pai/6
=>
-√3<= cotα <=√3
cosαsinβ
=sinαsinβ*cotα
=1/2*cotα
=>
-√3/2<=cosαsinβ<=√3/2