I think I have this problem down but then again I'm not sure. If you could check my work, please:
cot^2x = 1-2cscx+csc^2x
csc^2x-1 = 1-2cscx+csc^2x (from the pythag. identity)
0 = 2-2cscx + csc^2x-csc^2x
0 = 2-2cscx
0 = -1+cscx (divided all by -2)
cscx = 1
Also, I am so stuck on the following two. I have to use the double (or half, but I'm sure it's double) angle formulas but I don't know how to properly incorporate them:
1. 2cos^2x-1 = cosx
and
2. cos2x + 6sin^2x = 2
Help would be very much appreciated. Thank you!