Let f(x)=2x(sinx+tanx)2x+21ππ−41,x≠nπ, then f is (where [ . ] represents greatest integer function)

The denominator is=2x+21ππ−41=2xπ+21−41=221+xπ−41=2xπ+1∴ f(x)=x(sinx+tanx)xπ+12⇒f(−x)=−xsin(−x)+tan(−x)−xπ+12=x(sinx+tanx)−1−xπ+12=−x(sinx+tanx)xπ+12=−f(x)