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The value of lim(x-> pi/3) ((tan^3x-3*ta...

The value of `lim_(x-> pi/3) ((tan^3x-3*tanx)/cos(x+pi/6))`

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`lim_(x->pi/3)(tan^3x-3tanx)/(cos(x+pi/6))`
`L'`Hospital rule
`lim_(x->pi/3)(3tan^2x*sec^2x-2sec^2x)/(-sin(x+pi/6))`
`=lim_(x->pi/3)(3sec^2x(tan^2x-1))/(-sin(x+pi/6))`
By subtituting`x=pi/3` for finding limit value
`=(3sec^2(pi/3)[tan^2(pi/3)-1])/(-sin(pi/3+pi/6)`
`tan(pi/3)=sqrt3`
`sec(pi/3)=2`
...
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