SOLUTION: Please help me to solve this question {{{2*cos^2(A)=1+2*sin(A)cos(A)}}}
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Question 1014769: Please help me to solve this question
Found 2 solutions by ikleyn, solver91311:
Answer by ikleyn(52864) (Show Source): You can put this solution on YOUR website!
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Please help me to solve this question =
----------------------------------------------------
What question?
Where is no any question in your post.
If you think that your formula is an identity, then you are wrong.
The counter example is A=0.
Then the left side is 2, while the right side is 1.
If you want we consider it as an equation, then say explicitly and directly "Please help me to solve this equation".
So, edit and re-submit.
If you want to get an answer.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ 1\ +\ 2\sin(A)\cos(A))
I presume you want to solve for A. In the future, be specific about what you want; none of us are mind readers.
Add 
to both sides
\ -\ 1\ =\ 2\sin(A)\cos(A))
But \ -\ 1\ = \cos(2A))
and \cos(A)\ =\ \sin(2A))
, so:
\ =\ \sin(2A))
Square both sides:
\ =\ \sin^2(2A))
Use the Pythagorean Identity:
\ =\ 1\ -\ \cos^2(2A))
\ =\ 1)
\ =\ \frac{1}{2})
\ =\ \pm\frac{\sqrt{2}}{2})
\ =\ \frac{\pi}{4}\ +\ \frac{k\pi}{2}\ \forall\ k\ \in\ \mathbb{Z})
But if 
is odd, the root is extraneous, so:
John
My calculator said it, I believe it, that settles it
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