Question

How do you verify `csc^2(theta)(1-cos^2(theta))=1`?

Answer 1

True

Explanation:

`csc^2(theta)*(1-cos^2(theta))=1`

1) Solve on the left side. Notice the Pythagorean Identity.

`1-cos^2(theta) = sin^2(theta)`, this is just a jumbled version of `sin^2x +cos^2x = 1` identity.

2) implement the new value so that everything is sine on the left side.

`1/sin^2(theta)*sin^2(theta)/1 -> sin^2(theta)/sin^2(theta) -> 1`

It sounds like you just need to memorize the identities so you can spot them more easily in the future.