This is actually many steps through a calculus problem involving trig functions. I have not included the problem because I'm trying very hard to figure it out on my own (at least as far as it's possible). I've found the answer I'm looking for, but it's attached to a bunch of random junk. I'll be fine as long as the following identity is true:
2(tanx(sinx)^2-cotx(cosx)^2) + 2(tanx+cotx) + (tanx)^2 + (cotx)^2 + 2 = 0
Problem is, I just can't seem to make it work. I've triple-checked all the steps up to this point, so I'm pretty confident that the numbers here are correct. Is there any way that the above identity is true?
(cosx)^2+(sinx)^2 = 1
(tanx)^2 + 1 = (secx)^2
(cotx)^2 + 1 = (cscx)^2
The Attempt at a Solution
Working piecemeal, trying to find hidden identities within the above equation. For instance:
dividing 2sinxcosx from (2cotx-cotx(cosx)^2) produces 2sinxcosx((cscx)^2-(cotx)^2=2sinxcosx(1)=sin2x
I can also find both (1+(tanx)^2) and (1+cotx)^2) in the equation, producing (secx)^2 and (cscx)^2. However, none of these seem to be steps in the right direction.
It seems like what I need is to find some way to pull -2 out of an identity that equals 1, which would allow me to get rid of that 2 on the end. Then I need to arrange the rest of the identities so that they equal zero. I'm beginning to suspect this isn't possible, but my brain just can't let go.