已知sin(x+π/6)sin(x-π/6)=11/20,则tanx的值为?

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已知sin(x+π/6)sin(x-π/6)=11/20,则tanx的值为?
已知sin(x+π/6)sin(x-π/6)=11/20,则tanx的值为?

已知sin(x+π/6)sin(x-π/6)=11/20,则tanx的值为?
sin(x+π/6)sin（x-π/6）=[(根号3/2）sinx+1/2cosx][(根号3/2)sinx-1/2cosx]
=3/4(sinx)^2-1/4(cosx)^2=11/20.
故3(sinx)^2-(cosx)^2=11/5
(sinx)^2+(cosx)^2=1
联立方程组,可得(sinx)^2=4/5,(cosx)^2=1/5,tanx=根号(0.8/0.2)=2,


sin(x+π/6)sin(x-π/6)
=(sinxcosπ/6+cosxsinπ/6)(sinxcosπ/6-cosxsinπ/6)
=(sinxcosπ/6)^2-(cosxsinπ/6)^2
=3/4sin^2x-1/4cos^2x
=1/4(3sin^2x-cos^2x)
=1/4(3sin^2x-1+sin^2x)
=1/4(4sin^2x-1)=11/20
sin^2x=4/5
cos^2x=1-sin^2x=1/5
tan^2x=4
tanx=±2

如图

2,sinx=2√5/5 cosx=√5/5

用公式：sin(x+y)sin(x-y)=(sinx)^2-(siny)^2，可以化简运算。

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