lf the fundamental period of function `f(x)=sinx + cos(sqrt(4-a^2))x` is `4pi`, then the value of a is/are

Options

A. `(sqrt(15))/(2)`
B. `-(sqrt(15))/(2)`
C. `(sqrt(7))/(2)`
D. `-(sqrt(7))/(2)`

Answer

A, B, C, D

Explanation

Period of `sinx " is " 2pi` and period of `cos (sqrt(4-a^(2))x) " is " (2pi)/(sqrt(4-a^(2))).`
`implies LCM (2pi,(2pi)/(sqrt(4-a^(2))))=4pi` (given)
i.e., `sqrt(4-a^(2))=(p)/(2) " where " p=1,3.`
Hence ` a^(2) =(15)/(4),(7)/(4),a=+-(sqrt(15))/(2),+-(sqrt(17))/(2)`