SOLUTION: I am having a very hard time proving this identity sin 2x + sin 4x/cos 2x - cos 4x = cot x. If someone could help me that would be great. Also if you could break it down f

Algebra ->  Trigonometry-basics -> SOLUTION: I am having a very hard time proving this identity sin 2x + sin 4x/cos 2x - cos 4x = cot x. If someone could help me that would be great. Also if you could break it down f      Log On


   

Question 131980: I am having a very hard time proving this identity
sin 2x + sin 4x/cos 2x - cos 4x = cot x.
If someone could help me that would be great. Also if you could break it down for me and explain what you did I would be very grateful. I have tried doing it several ways and can not figure it out.
Thanks so much.
Answer by TakeATuition.com(57) About Me  (Show Source):
You can put this solution on YOUR website!
SOLUTION -

%28Sin2x%2Bsin4x%29%2F%28cos2x-cos4x%29=cotx
Taking L.H.S we have
[2sin%28%282x%2B4x%29%2F2%29cos%28%282x-4x%29%2F2%29]/[-2sin%28%282x%2B4x%29%2F2%29sin%28%282x-4x%29%2F2%29]
{ (since sinc%2Bsind=2sin%28%28c%2Bd%29%2F2%29cos%28%28c-d%29%2F2%29
cosc-cosd=-2sin%28%28c%2Bd%29%2F2%29sin%28%28c-d%29%2F2%29}
=%282sin3xcos%28-x%29%29/%28-2sin3xsin%28-x%29%29
=cosx%2Fsinx {since cos(-x)=cosx and sin(-x)=-sinx}
= cotx

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