The period of the function f(x) = sin2πx+(sinπx/3)+(sinπx/5) is (A) 2(B) 6(C) 15(D) 30

Answer:D. First of all, the observation to be done is that the period of sine curve is 2π. When any number is multiplied within the parenthesis of sin(x) then it`s period will become 2π/(that number). (To help you in understanding in a better way, let me show u an example: sin(2x) will have a period of 2π/2 = π. ). Now, coming back to the question, sin(2πx) will have a period of 1, sin(πx/3) will have a period of 6 and sin(πx/5) will have a period of 10. Now their is one more important theory To be known. When a function is written in terms of many different other functions of same or different periods, then the period of the given function will be L.C.M of all those periods. (For example: f(x) = sin(2x) + sin(x), then the period of f(x) will be L.C.M of π and 2π which is 2π.). So in this question the answer is L.C.M of 1, 6 and 10 which is 30.