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December 22, 2014

December 22, 2014

Posted by **Nikki** on Sunday, July 15, 2012 at 5:48pm.

cos^2(x) = sin^2(x/2)

- Trigonometry -
**Damon**, Sunday, July 15, 2012 at 6:00pmsin (x/2 ) = + sqrt([1-cos x]/2) if x/2 in q 1 or 2 thus if 0 < x < 2 pi

sin^2 (x/2) = [1-cos x]/2

so

cos^2 x = [1 - cos x]/2

2 cos^2 x = 1 - cos x

2 cos^2 x + cos x = 1

let z = cos x

2 z^2 + z -1 = 0

(2 z - 1)(z +1) = 0

z = cos x = 1/2

or cos x = -1

x = 60 deg (pi/3) or -60 deg (5 pi/3)

or x = 180 deg (pi)

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