Question

`lim_(xrarr0) ((1-cos2x)^2)/(2xtanx-xtan2x)` , is
A. 2
B. `-(1)/(2)`
C. `(1)/(2)`
D. `-2`

Answer 1

Correct Answer - 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))/(-2tan^3x)`
` =-2 lim_(xto0) ((sinx)/(x))cos^3x(-tan^2x)=-2xx1xx1=-2`