Final answer:
The trigonometric expression 8 cos(t) tan(t) simplifies to 8 sin(t) when rewritten in terms of sine and cosine.
Step-by-step explanation:
The trigonometric expression 8 cos(t) tan(t) can be rewritten in terms of sine and cosine and then simplified. We know that tan(t) is equivalent to sin(t)/cos(t). By substituting this into the original expression, we get:
8 cos(t) * (sin(t)/cos(t)) = 8 sin(t)
This simplification shows that 8 cos(t) tan(t) is equivalent to 8 sin(t) when expressed in terms of sine and cosine.
To write the expression 8 cos(t) tan(t) in terms of sine and cosine, we can use the identity tan(t) = sin(t) / cos(t). Substituting this into the expression gives us 8 cos(t) (sin(t) / cos(t)). Canceling out the cos(t) terms leaves us with 8 sin(t).
This expression can be simplified further by using the properties of sine and cosine. For example, we can use the identity sin^2(t) + cos^2(t) = 1 to simplify the expression if needed.