The function f(x)= k Isin xI + k2Icos xI +g(q) has period = pi/2, then k is:(a) 2 (b) 1 (c)3 (d) none of these. How?

Hi Aditi,

g(q) is a constant function, and hence always periodic.

So the period of k|sinx| + k²|cosx| should be pi/2.

Which is possible only when k=1

Since the period of f(x) = |sinx| + |cosx| is pi/2

Note that f(x+pi/2) = f(x) for k=1 only.

Hence Option (B).

Hope that helps.

Best Regards,

Ashwin (IIT Madras).