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 trigonometric 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:
$=\sin{(-t)} - \cos{(-t)} - \tan{(-t)}$
RECALL:
(1) $\sin{(-t)} = -\sin{t}$
(2) $\cos{(-t)} = \cos{t}$
(3) $\tan{(-t)} = -\tan{t}$
Use the given and rules above to obtain:
$=-\sin{t} - \cos{t} -(-\tan{t})
\\=-\sin{t} - \cos{t} + \tan{t}
\\=-a -b + c$
