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Old May 4th 2014, 10:29 PM   #1
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Physics and mathematics

Root[2A^2(1 Cos theta)]=root[4A^2 cos^2 theta /2]
Could you please explain this.
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Old May 5th 2014, 06:03 AM   #2
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You seem to be missing an important '+' sign, and didn't use parentheses as needed, but I think what you mean is this:



To show this is true start by cancelling out the square root sign and 2A^2 from both sides, leaving:



Now substitute 2*alpha for theta, and use the double angle formula for cosine:



All that remains is some minor rearrangement and resubstitute theta for alpha. Also note that because of the square root signs this is true only for positive values of cos(theta/2): -pi <= theta <= +pi.

Last edited by ChipB; May 5th 2014 at 10:30 AM.
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