prove (cos4x+cos3x)/(sin4x-sin3x) = cotx/2 Can anyone help me explain the answer please

Question

anonymous · Answer

cos4x + cos3x = 2cos(7x/2)cos(x/2)
sin4x - sin3x = 2cos(7x/2)sin(x/2)
Their division is given.
On dividing cos(7x/2) Cancels out.
We are left with.
cos(x/2) / sin(x/2) = cot(x/2)

anonymous · Answer

@siddhantsharan you typed fast!!!

anonymous · Answer

HAha. Thanks. :D

anonymous · Answer

how did you get 2cos(7x/2)cos(x/2)

anonymous · Answer

someone help me pleaseeee

anonymous · Answer

are the 4 and 3 meant to be exponents?

anonymous · Answer

nooo

anonymous · Answer

Then it's not an identity, you can't prove it.

anonymous · Answer

but i got the first answer

anonymous · Answer

I just wolfram alphad it, it's not an identity.

anonymous · Answer

how do you do it then?

dumbcow · Answer

http://www.mathwords.com/s/sum_to_product_identities.htm the 1st post has it correct, here is how they came up with it

anonymous · Answer

you're saying wolfram alpha is wrongggggggggg?

dumbcow · Answer

i am, haha
post the link

anonymous · Answer

OMG thank you! i dont have that pellet on my identity sheet

dumbcow · Answer

welcome, yeah i never learned these identities very well either