Yep just multiply top and bottom by -1. You've done all the hard work! Well done.
I have to find the first derivative of y= ln((1-cos(x))/(1+cos(x)))
the derivative of the ln is 1+cos(x)/1-cos(x)
and the derivative of the inner function is:
((1+cosx) (sinx) - (1-cos(x) (-sinx)
-----------------------------------
(1+cos(x))^2
i then multiplied and got
(1+cos(x))(sinx + sinxcosx+sinx-sinxcosx)
----------------------------
(1+cos(x))^2 * 1-cos(x)
to clean this up:
2sinx * (1+cos(x))
---------------------------- = y'
(1+cos(x))^2 * 1-cos(x)
After canceling out stuff:
2sinx
------------------- = y'
1-cosx^2
but the answer says:
- 2sinx
------------------- = y'
cosx^2-1
Is this merely a matter of just multiplying both of these by -1??