The correct option is
B f(x)=sinx+cos2xOption A,
f(x)=sin(2πx+π3)+2sin(3πx+π4)+3sin5πxPeriod of
sin(2πx+π3) is
2π2π=1Period of 2sin(3πx+π4)is 2π3π=23
Period of 3sin5x is 2π5π=25
LCM of 1,23,25=LCMof1,2,2HCFof3,5=2
So, period of f(x) is 2.
B) f(x)=sinπx3+sinπx4
Period of sinπx3 is 2ππx3=6
Period of sinπx4 is 2ππx4=8
LCM of 6 and 8 is 24.
So, period of f(x) is 24.
C) f(x)=sinx+cos2x
Period of sinx is 2π
Period of cos2x is 2π2=π
LCM of 2π,π is 2π
Hence, period of f(x) is 2π
∴ Period of f(x)=sinx+cos2x=2π