Question

How do you find the limit of `(1 - cos(2x)) / (x sin(2x))` as x approaches `0`?

Answer 1

`1`.

Explanation:

The Nr.`=1-cos2x=2sin^2x` and,

Dr.`=xsin2x=2xsinxcosx`

Hence,`lim_(xrarr0){(2sin^2x)/(2xsinxcosx)}`

`lim_(xrarr0){(sinx)/(xcosx)}`

`lim_(xrarr0){(sinx/x)*(1/cosx)}`

`=1`.