The period of the function f(x)=[8x+7]+∣tan⁡2πx+cot2πx∣−8x (where [.] denotes the greatest integer function), is _______.

f(x)=[8x+7]+|tan⁡2πx+cot⁡2πx|−8x=[8x]−8x−7+|tan⁡2πx+cot⁡2πx|=−{8x}+|tan⁡2πx+cot⁡2πx|+7Period is {8x} is 1/8. Also, |tan⁡2πx+cot⁡2πx|=sin⁡2πxcos⁡2πx+cos⁡2πxsin⁡2πx=1sin⁡2πxcos⁡2πx=|2cosec⁡4πx|Now, period of 2 cosec 4πx is 1/2. Then period of |2cosec⁡4πx| is 1/4.Therefore, period is L.C.M. of 18 and 14 which is 14.