If `i_(1) = i_(0) sin (omega t), i_(2) = i_(0_(2)) sin (omega t + phi)`, then `i_(3) =`

Options

A. `sqrt(i_(0_(1))^(2) + i_(0_(2))^(2)) sin {phi + omega t}`
B. `(i_(0_(1)) + i_(0_(2))) sin ((phi)/(2) + omega t)`
C. `(sqrt(i_(0_(1))^(2) + i_(0_(2))^(2) + 2i_(0_(1)) i_(0_(2)) cos phi)) sin [phi + omega t]`
D. `(sqrt(i_(0_(1))^(2) + i_(0_(2))^(2) + 2i_(0_(1)) i_(0_(2)) cos phi)) sin [alpha + omega t]` where `alpha=Tan^(-1) [(i_(0_(2)) sin phi)/(i_(0_(1))+i_(0_(2)) cos phi)]`

Answer

D

Explanation

Apply principle of superposition