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anonymous
 5 years ago
Can someone show me why cos^2(x) is equal to (1/2)cos(2x) + 1/2 ?
anonymous
 5 years ago
Can someone show me why cos^2(x) is equal to (1/2)cos(2x) + 1/2 ?

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shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0*sigh* Ignore RodneyF.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wolfram says it's true... don't know how in the world that is true.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0There's a few reasons you can show depending on your understanding. There's the \(e^{i\theta}\) argument, or there's the angle addition arguement. Which would you prefer?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Its basically a derivative of the double angle formula for sin and cos. I can have a go at writing the proof out, but you may be better to google it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0There is no algebraic way? hmm..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0There is. Its just quite fiddly

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0There is, using the sum of angles formula.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0cos (2x) = cos^2(x)  sin^2(x) cos(2x) + sin^2(x) = cos^2(x) cos (2x) + 1  cos^2(x) = cos^(x) cos(2x) +1 = 2cos^2(x) cos(2x)/2 + 1/2 = cos^2(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But doesn't that assume the prior knowledge of that trig identity?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Was just about finished with mine.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Or doesnt that matter?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It assumes you know the addition of angles identity yes.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'm in calc.. should have known that identity.. Always forget important stuff...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sin 2a= sin ( a+a ) = sin a cos a + cos a sin a = 2 sin a cos a. cos 2 a= cos ( a+a ) = cos a cos a − sin a sin a cos 2a = cos² a− sin²a. . . . . . . (1) This is the first of the three versions of cos 2a. To derive the second version, in line (1) use this Pythagorean identity: sin²a = 1 − cos²a. Line (1) then becomes cos 2a = cos²a − (1 − cos²a) = cos²a − 1 + cos²a. cos 2a = 2 cos²a − 1. . . . . . . . . . (2) To derive the third version, in line (1) use this Pythagorean identity: cos² a= 1 − sin²a. We have cos 2 a= 1 − sin² a− sin²a;. cos 2a = 1 − 2 sin²a. . . . . . . . . . (3) These are the three forms of cos 2a.

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0cos(x+x)=cos(x)cos(x)sin(x)sin(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[cos(\theta + \phi) = cos(\theta)cos(\phi)  sin(\theta)sin(\phi)\] So if \(\theta = \phi\) you start getting things simplified very quickly.
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