求极限.准确.lim(x>2分之派) tan3x分之tanx

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lim(x→π/2) tanx/tan3x
=lim(x→π/2) sec^2x/[3sec^2(3x)]
=lim(x→π/2) cos^2(3x)/(3cos^2x)
=lim(x→π/2) 2cos(3x)sin(3x)/(6cosxsinx)
=lim(x→π/2) cos(3x)/cosx
=lim(x→π/2) -3sin(3x)/(-sinx)
=9

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