for all values for which the following is defined, find the value of cot^2(theta)-csc^2(theta)

Answer 1

Substituting
cot(θ)=cos(θ)/sin(θ)
and csc(θ) = 1/sin(θ)
you will have a common denominator of
sin²(θ).
Add the numerators and use
cos²(θ)+sin²(θ) = 1
to simplify further.

Answer 2

so wwould the anser be -1/sin(theta)
because it would be cos^2(theta)-1/ sin^2(theta) and then simnplify

Answer 3

"so wwould the anser be -1/sin(theta)
because it would be cos^2(theta)-1/ sin^2(theta) and then simnplify"

It is unfortunate that insufficient use of parentheses leads to mathematical errors.

The expression is correct if we insert parentheses at the right places.

Instead of cos^2(theta)-1/ sin^2(theta), it should be
(cos^2(theta)-1)/ sin^2(theta)
= -sin^2(theta)/sin^2(theta)
= -1