Express Cos (x/2) in terms of Cos x?

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2007-11-24 10:46:59 · 4 answers · asked by sohan s 1 in Science & Mathematics ➔ Mathematics

cos (x/2) = +/- sqrt ((1+cos(x))/2)

2007-11-24 10:56:55 · answer #1 · answered by Anonymous · 0⤊ 0⤋

And you can prove their answers by writing cos(x) as cos (x/2 + x/2) and using the sum formula on that, along with [sin(@)]^2 + [cos(@)]^2 = 1.

2007-11-24 19:14:07 · answer #2 · answered by ted s 7 · 0⤊ 0⤋

Since cos2A = 2(cosx)^2 - 1
Hence,

cosx = 2(cos(x/2))^2 - 1
cosx + 1 = 2(cos(x/2))^2
(cosx + 1)/2 = (cos(x/2))^2
sqrt[(cosx + 1)/2] = cos(x/2)

2007-11-24 19:25:27 · answer #3 · answered by Kemmy 6 · 0⤊ 0⤋

This is the half angle formula

cos(x/2) = Â±â[(1 + cosx) / 2]

2007-11-24 18:57:23 · answer #4 · answered by Northstar 7 · 0⤊ 0⤋