Answer:
*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.