Question

Simplify sin(t) cot(t) to a single trig function.

a) cos(t)
b) tan(t)
c) csc(t)
d) sec(t)

Answer 1

Sin(t) cot(t) simplifies to cos(t) by using the definition of cotangent as the reciprocal of tangent, which further simplifies to cosine after cancelling out sine functions.

Step-by-step explanation:

To simplify sin(t) cot(t) to a single trigonometric function, we need to recall the definition of the cotangent function. Cotangent is the reciprocal of the tangent function, which means that cot(t) = \frac{1}{tan(t)}. The tangent function is the ratio of sine to cosine, so tan(t) = \frac{sin(t)}{cos(t)}. Using these identities, we can rewrite the original expression.

sin(t) cot(t) = sin(t) * \frac{1}{tan(t)} = sin(t) * \frac{cos(t)}{sin(t)}

Now, we can see that the sine functions will cancel each other out, leaving us with cos(t).

Therefore, sin(t) cot(t) simplifies to cos(t).