If the period of `(cos(sin(n x)))/(tan(x/n)),n in N ,i s6pi` , then `n=` (a) 3 (b) 2 (c) 6 (d) 1

Options

A. 3
B. 2
C. 6
D. 1

Answer

C

Explanation

The period of `cos(sin n x) " is " (pi)/(n) ` and the period of `"tan"((x)/(n))` is `pi` n.
Thus, `6pi=LCM ((pi)/(n),pi n)`
` or 6pi=(pi)/(n) lambda_(1) or n =(lambda_(1))/(6),`
` and 6pi =lambda_(2)pi n or n=(6)/(lambda_(2)),lalmbda_(1),lambda_(2) in I^(+)`
From `n =(6)/(lambda_(2)), n=6,3,2,1.`
Clearly, for `n=6`, we get the period of `f(x)` to be `6pi`.