Question

How do you simplify the expression `cot^2theta-csc^2theta`?

Answer 1

-1

Explanation:

Since `cot theta=cos theta/sin theta` and `csc theta=1/sin theta`,

the given expression becomes:

`cos^2 theta/sin^2 theta-1/sin^2 theta=`

`(cos^2 theta-1)/sin^2 theta`

Then, since `sin^2 theta=1-cos^2 theta`, it becomes:

`-cancel(sin^2 theta)/cancel(sin^2 theta)=-1`