Evaluate `lim_(x to0)(xtanx)/((1-cosx))`

1.	Evaluate `lim_(x to0)(xtanx)/((1-cosx))`
Answer» `lim_(x to 0)(x tanx)/((1-cosx))=lim_(xto0)(x tanx)/(cos x(1-cosx))` `=lim_(x to 0)(x sin^(2)x)/(sinx cos x(1-cosx))` `=lim_(x to 0)(x(1-cos^(2)x))/(sinx cosx(1-cosx))=lim_(x to 0)(x(1+cosx))/(sin x cosx)` `=lim_(xto0)(x)/(sinx)lim_(xto0)((1+cosx))/(cosx)=(1xx(2)/(1))=2.`

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