Consider a nonlinear inductor which is defined by $\phi = i + tanh (i)$. Let the current through this inductor be i(t) = sin t. Find the voltage across it (see <image 1>).
['$[1 + sech^2 (sin t)] cos t$', '$[1 + sech^2 (sin t)] sin t$', '$[1 - sech^2 (sin t)] sin t$', '$[1 - sech^2 (cos t)] sin t$']