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lim(xrarr0) ((1-cos2x)^2)/(2xtanx-xtan2x...

`lim_(xrarr0) ((1-cos2x)^2)/(2xtanx-xtan2x)` , is

A

2

B

`-(1)/(2)`

C

`(1)/(2)`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
D
`lim_(xto0) ((1-cos2x)^2)/(2xtanx-xtan2x)`
`=lim_(xto0) (4sin^4x)/(x(2tan x-(2tanx)/(1-tan^2x)))`
` =lim_(xto0) (4sin ^4x(1-tan^2x))/(-2xtan^3x)`
` =-2 lim_(xto0) ((sinx)/(x))cos^3x(-tan^2x)=-2xx1xx1=-2`
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