Let sin t = a, cos t = b, and tan t = c. write the expression in terms of a, b, and c.
-sin(-t - 8 π) + cos(-t - 2 π) + tan(-t - 5 π)

*Note c could be written as a/b

Step-by-step explanation:

-sin(-t - 8 π) + cos(-t - 2 π) + tan(-t - 5 π)

The identities I'm about to apply:

Let's apply the difference identities to all three terms:

We are about to use that cos(even*pi) is 1 and sin(even*pi) is 0 so tan(odd*pi)=0:

Cleaning up the algebra:

Cleaning up more algebra:

Applying that sine and tangent is odd while cosine is even.  That is,

sin(-x)=-sin(x) and tan(-x)=-tan(x) while cos(-x)=cos(x):

Making the substitution the problem wanted us to:

Just for fun you could have wrote c as a/b too since tangent=sine/cosine.