Simplify sin squared 𝜃 plus cos squared 𝜃 divided by csc squared 𝜃 minus cot squared 𝜃.
There are a few trig identities that will help us simplify this expression. We know that sin squared 𝜃 plus cos squared 𝜃 is equal to one. So we can actually replace the numerator with one.
And now looking at the denominator, we have csc squared 𝜃 and cot squared 𝜃, csc squared 𝜃 is equal to cot squared 𝜃 plus one. So we can replace csc squared 𝜃 with this. So now we need to add to the bottom the minus cot squared 𝜃.
So now we have one divided by cot squared 𝜃 plus one minus cot squared 𝜃. So the cot squared 𝜃s cancel, and we are left with one over one. And one divided by one is one.
So it simplifies to be one.