SOLUTION: proove that 1/sin2A+cos4A/sin4A=cotA-cosec4A

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Question 972445: proove that 1/sin2A+cos4A/sin4A=cotA-cosec4A
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
1%5E%22%22%2Fsin%282A%5E%22%22%29%2Bcos%284A%5E%22%22%29%2Fsin%284A%5E%22%22%29%22%22=%22%22cot%28A%5E%22%22%29-csc%284A%5E%22%22%29

First we work with the left side:


Get LCD




--------------------------------

Now we work with the right side:

cot%28A%5E%22%22%29-csc%284A%5E%22%22%29

There is an identity tan%28x%2F2%29%22%22=%22%22sin%28x%5E%22%22%29%2F%281%2Bcos%28x%5E%22%22%29%29
We can flip both sides and get

cot%28x%2F2%29%22%22=%22%22%281%2Bcos%28x%5E%22%22%29%29%2Fsin%28x%5E%22%22%29

If we let A=x%2F2 and therefore x=2A, we get

cot%28A%5E%22%22%29%22%22=%22%22%281%2Bcos%282A%5E%22%22%29%29%2Fsin%282A%5E%22%22%29

So the right side of the identity that we are to prove becomes:

%281%2Bcos%282A%5E%22%22%29%29%2Fsin%282A%5E%22%22%29-csc%284A%5E%22%22%29

%281%2Bcos%282A%5E%22%22%29%29%2Fsin%282A%5E%22%22%29-1%5E%22%22%2Fsin%284A%5E%22%22%29



Get LCD:





We have worked each side separately to the same expression.
So we have proved the identity.

Edwin