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lim(x->0)(1-cos2x+tan^2x)/(xsinx)...

`lim_(x->0)(1-cos2x+tan^2x)/(xsinx)`

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`lim_(x->0)(1-cos2x+tan^2x)/(xsinx)`

We know,

`(lim)_(x->0) (sin x)/(x)=1`

`(lim)_(x->0) (tan x)/(x)=1`

`(lim)_(x->0) (1-cosx)/(x^2)=1/2`

`lim_(x->0)(1-cos2x+x^2)/(x*x)`

`lim_(x->0)(1-cos2x)/(x^2)+(x^2)/(x^2)`

`=4*1/2+1=2+1=3`

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