SOLUTION: Hello, I was hoping you could help me verify this identity. I'm actually really good at the various identities and verifying them, but this problem is proving really complex for me

Question 829183: Hello, I was hoping you could help me verify this identity. I'm actually really good at the various identities and verifying them, but this problem is proving really complex for me and I just can't seem to get through it. I was hoping you could really show me step-by-step on how to get the answer for this problem.
It is:

Thank you for your help in advance, I appreciate you taking the time to assist.
Found 2 solutions by stanbon, lwsshak3:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
((cos(a)-cos(b))/(sin(a)+sin(b)))+((sin(a)-sin(b))/(cos(a)+cos(b)))= 0
==========
numerator:: {[cos(a)+cos(b)][(cos(a)-cos(b)] + [sin(a)+sin(b)(sin(a)-sin(b)]}
denominator: (sin(a)+sin(b))(cos(a)+cos(b))
--------
numerator:: [cos^2(a)-cos^2(b)] + [sin^2(a)-sin^2(b)]
denominator: no change
---------
numerator:: [cos^2(a)+sin^2(a) -(cos^(b)+sin^2(b)]
denominator:: no change
----
numerator:: [1 + 1] = 2
denominator: no change
------
Equation after changes::
2/(sin(a)+sin(b))(cos(a)+cos(b)) = 0
------------------
2 = 0
If I have made no mistakes, there is no solution.
==========================
Cheers,
Stan H.
==========================
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!

verified: left side=right side
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