Question

Simplify cos(t)tan(t) to a single trig function or constant with no fractions.

a) sin(t)
b) cot(t)
c) csc(t)
d) sec(t)

Answer 1

To simplify cos(t)tan(t), rewrite tan(t) as sin(t)/cos(t). The terms cos(t) cancel out, leaving sin(t) as the simplified form.

Step-by-step explanation:

To simplify cos(t)tan(t) to a single trigonometric function or constant without fractions, we need to understand how the trigonometric functions relate to each other. The tangent of an angle is defined as the ratio of the sine to the cosine of that angle:

tan(t) = sin(t) / cos(t)

Using this definition, we can rewrite the expression as:

cos(t) * (sin(t) / cos(t))

When we multiply cos(t) by sin(t) / cos(t), the cos(t) in the numerator and the denominator will cancel out, leaving us with:

sin(t)

Thus, the simplest form of cos(t)tan(t) is sin(t), which means the correct answer is option (a).

To simplify cos(t)tan(t) to a single trig function or constant with no fractions, we can use the trigonometric identity: tan(t) = sin(t)/cos(t). Plugging this identity into the expression, we get: cos(t) * sin(t)/cos(t). The cosine terms cancel out, leaving us with sin(t). Therefore, the correct answer is option a) sin(t).