If 2f(x)+xf(1x)−2f2sin⁡πx+14=4cos2⁡πx2+xcos⁡πx,∀x∈R−{0},which of the following statement(s) is/are true?

Replacing x by 2,  ⇒ 2f(2)+2f12−2f(1)=4 ⇒ f(2)+f12=2+f(1)Replacing x by 1,f(1)=−1Replacing x by 12,2f12+12f(2)+2=522f(2)+12f12=12From Eqs.(i) and (ii), we getf(2)=1,f12=0