$S_1$ and $S_2$ are two sources of light which produce individually disturbance at a point P given by $\in _1=3 \sin wt,\;\in _2 =4 \cos wt$ Assuming $\overrightarrow {\in_1}$ and $\overrightarrow{\in_2}$ to be along the same line then result of their superposition is

Question

$(a)\;5 \sin (wt+\tan^{-1} 4/3) \\ (b)\;5 \sin (wt) \\ (c)\;5 \sin [2wt+2 \tan^{-1} 4/3] \\ (d)\;5 \sin [ \tan^{-1} 4/3]$