Answer
$a + b - c$
Work Step by Step
Note that the angles $t+2\pi$ and $t + 4\pi$ are both coterminal with the angle $t$ since $2\pi$ and $4\pi$ are multiples of $2\pi$.
Note further that coterminal angles have the same value for the trignomoetric functions.
Thus, the given expression is equivalent to
$=\sin{t} + \cos{t} - \tan{(t+\pi)}$
Recall that the period of the tangent function is $\pi$. This means that the angles $t$ and $t+\pi$ have the same value as they are one period apart.
Thus, the expression above is equivalent to:
$=\sin{t} + \cos{t} - \tan{t}$
Use the given to obtain:
$=a + b - c$
