The function f (x) = k |cos x| + k² |sin x| + $\mathrm{\varphi }$(k) has period $\frac{\mathrm{\pi }}{2}$ if k is equal to

Since |sin x| + |cos x| is a periodic function with period $\frac{\mathrm{\pi }}{2}$ therefore period of f (x) will be $\frac{\mathrm{\pi }}{2}$ when k = 1.