Prove the Identity:
What do I do after I have all of this done?
See my response to your other post:
and take it to heart. Also Plato's step by step proof in the same thread offers an example of the correct way to do this type of problem.
Notice that the right hand side of the equation you have a double-angle and on the right hand side you have a single angle . This should give you a hint that you will probably have to use a double-angle identity. Perhaps:
Or as mr. fantastic pointed out one of the many other double angle identities (his, in fact, is easier to apply).
Arriving at the conclusion that 1 = 1 by starting with -1 = 1 and manipulting both sides of the equation is wrong.
The proof should go like this:
(write down left hand side of equation)
(by the fact that )
(by finding a common denominator and simplifying)
(by the identities mr. fantastic gave)
(end with the right hand side of the equation)
This is fundamentally different from the approach you took.
You know that .
You have in your bottom expression which resembles the expression above except you're missing that factor of 2. So if you want to use that factor of 2, you must counter it by multiply by 1/2 (since 1/2 x 2 = 1).
To see it algebraically, divide both sides by 2 of the first expression to get:
To me it just seems like that number just appears there without question. That is what I'm saying. I don't think it goes back to algebra, because I am very good algebra. I'm still confused but I will agree with what you are saying. But really all I was saying was I do not get how you go from this step to this I know that you use identities. But it randomly seems like a 2 and 1/2 are put in there for no reason. Just seems to me as this way to go about proving the identity is more complicated then what I said, which in turn is confusing me which is right and which is wrong.