please simplify to an expression involving a single trig function with no fractions.

Question

1 - sin²(t) / sin²(t)

Answer 1

Let's start this off by stating some important identities:

1. cos²(t) + sin²(t) = 1
2. cos²(t) / sin²(t) = cot²(t)

Now that we have our trusty equations, let's return to the problem:

1 - sin²(t) / sin²(t)

Well, if identity 1. is true, then we must have that 1 - sin²(t) = cos²(t). Substituting this in, we are left with cos²(t) / sin²(t), which is equal to cot²(t) by identity 2.

Thus, the equivalent expression is cot²(t).

Answer 2

Use the identity 1-sin^2 = cos^2

so this is cos^2/sin^2 which is cot^2(x)