look, it's easy :

first when x tends from positive side to zero.

greatest integer of cosx will result in zero =>sin0 =0 absolutely,

now for negative side,

as cos is positive in first and 4th quad.

and it's value is always less than 1,

so, it again results in zero when greatest integer is applied to it.

So, everytime your numerator is ablsolutely, Sin0, means 0.

Hence, the ans.

Hope you got it now. :)