Use phasor techniques to find an expression for i(t) expressed as a single cosine function, where i(t)=[250cos(377t+30∘)−150sin(377t+ 140∘)] ma

Using your favorite vector calculator, you can add
.. 250∠30° -150∠(140°-90°)
to get the sum
.. 120.512∠4.804°

Then i(t) = 120.512cos(377t +4.804°) ma

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The graph shows the individual currents, their sum, and the cosine function above, demonstrating that this is the solution.