If f(x)=x(sin⁡x+tan⁡x)[x+ππ]−12 , where [ ] denotes greatest  integer function, then

f(x)=x(sin⁡x+tan⁡x)[x+ππ]−12=x(sin⁡x+tan⁡x)[xπ]+1−12 =x(sin⁡x+tan⁡x)[xπ]+0.5⇒f(−x)=−x(sin⁡(−x)+tan⁡(−x))[−xπ]+0.5 ⇒f(−x)=x(sin⁡x+tan⁡x)−1−[xπ]+0.5,x≠nπ0,x=nπ   ⇒f(−x)=−x(sin⁡x+tan⁡x)[xπ]+0.5,when x≠nπ