Simplify csc ( t )/ cot ( t ) to a single trig function with no fractions.

Question

Simplify  to a single trig function with no fractions.

Answer 1

Hi!

The first thing is to think about other ways of writing these functions. csc = 1/sin and cot = 1/tan

So: (1/sin) / (1/tan)

we also know tan is sin/cos, which will be better to work with because we can use the sine in the numerator.

(1/sin) / [1/(sin/cos)]

simplifying the right side, the division 1/(sin/cos) is the same as the multiplication in 1/1 * cos/sin = cos/sin

Now we have: (1/sin) / (cos/sin), which is the same as:

1/sin * sin/cos

crosscut the sins and we get: 1/cos

And, as we know, 1/cos is the same as secant, so our answer is sec(t).

Hope that helped and let me know if you have any questions!