Let sin t = a, cos t = b, and tan t = c. write the following expression in terms of a, b, and c.

sin (t + 4pi) - cos (t + 8pi) + tan (t + 5pi)

We use the trigonometric identities in this problem.

=(sin(t)cos(4π)+sin(4π)cos(t))−(cos(t)cos(8π)−sin(t)sin(8π)) +tan(t)+tan(5π)/1−tan(t)tan(5π)
=sin(t)+0−cos(t)+0+ tan(t)1−0=sin(t)−cos(t)+tan(t)
=a−b+c