The period of the function f (x) = a sin kx + b cos kx is

We have, f (x) = a sin kx + b cos kx=a2+b2aa2+b2sin⁡kx+ba2+b2cos⁡kx=a2+b2(cos⁡θsin⁡kx+sin⁡θcos⁡kx)where cos⁡θ=aa2+b2=a2+b2sin⁡(kx+θ)which is a periodic function of period 2π|k|.