Question

If the function f (x)=sinx +cospx is periodic then p must be

Answer 1

Given :

Given function is :

f(x) = sinx + cospx

To Find :

If f(x)  is periodic then the value of p = ?

Solution :

Since we know that sinx is periodic function and also cosx is periodic .

∴The sum of two periodic functions is also periodic and the period of the new function ( i.e. the sum of two periodic functions)  is given as the LCM of the periods of the both the functions .

So , in order to get a LCM of the period of these two functions , 'p' must be irrational because the period of sinx is $\frac{\pi}{2}$ which is  irrational .

Hence , p must be an irrational number .