已知cosx/cos3x=3 ,求sinx/sin3x

三倍角公式
sin(3x)=3sinx-4(sinx)^3
cos(3x)=4(cosx)^3-3cosx
cosx/cos3x=3
cosx/(4(cosx)^3-3cosx)=3
1/(4(cosx)^2-3)=3
4(cosx)^2-3=1/3
4(cosx)^2=10/3
(cosx)^2=5/6
(sinx)^2=1-(cosx)^2=1/6
sinx/sin3x
=sinx/(3sinx-4(sinx)^3)
=1/(3-4(sinx)^2)
=1/(3-4*1/6)
=1/(3-2/3)
=1/(7/3)
=3/7