Answer
$V = 50~sin~(120\pi t+0.927295)$
Work Step by Step
We can use the following identity:
$a~sin~x+b~cos~x = \sqrt{a^2+b^2}~sin(x+y)$
where $y = tan^{-1}(\frac{b}{a})$
$V_1 = 30~sin~120\pi t$
$V_2 = 40~cos~120\pi t$
We can find $y$:
$y = tan^{-1}(\frac{b}{a})$
$y = tan^{-1}(\frac{40}{30})$
$y = 0.927295$
We can find an expression for $V$:
$V = V_1+V_2$
$V = 30~sin~120\pi t+40~cos~120\pi t$
$V = \sqrt{30^2+40^2}~sin~(120\pi t+0.927295)$
$V = 50~sin~(120\pi t+0.927295)$