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Evaluate lim(xto0) (cot2x-cosec2x)/(x)....

Evaluate `lim_(xto0) (cot2x-cosec2x)/(x).`

Text Solution

Verified by Experts

The correct Answer is:
-1
We have
`underset(xto0)lim(cot2x-cosec2x)/(x)`
`=underset(xto0)lim((cos2x)/(sin2x)-(1)/(sin2x))/(x)=underset(xto0)lim(cos2x-1)/(xsin2x)`
`=underset(xto0)lim(-(1-cos2x))/(xsin2x)=-underset(xto0)lim(2sin^(2)x)/(x(2sinxcosx))`
`=-underset(xto0)lim(tanx)/(x)=-1`
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