Half Angle Formulas.. Can anyone please answer Why Cos (x/2) = Cos x?

Answer 1

using geometry we can prove that
cos(a+b)= cos(a)cos(b)-sin(a)sin(b)
when a = b
cos(2a)=cos^2(a)-sin^2(a)=2cos^2(a)-1

what you stated in the question is not exactly correct.

Answer 2

It doesn't.
cos (x/2) = √(1/2)(1 + cos x))
The special case of
cos (x/2) = cos x
becomes
2cos^2 x - cos x - 1 = 0
(2cosx + 1)(cosx - 1) = 0
cosx = - 1/2, 1
x = 0°, 240°
or x = 0, 4π/3

Answer 3

I'm sorry, but I think you got it wrong. It's very obvious that the cos of x/2 is not the same as the cos of x since x/2 is NOT EQUAL to x.

But from trigometry, Cos (x/2) is equal to
+/- sqrt[(1 + cosx)/2]

teddy boy

Answer 4

cos (x) = cos( x/2 + x/2) = cos^2(x/2) - sin^2(x/2) = 2 cos^2(x/2) -1

If the formula you wrote is an equation (and it is certainly not an identity), we'll have

2 cos^2(x/2) -1 = cos(x/2),

a quadratic equation, whose unknown is cos(x/2)

cos(x/2) = (1 +/- sqrt(1 + 8)) / 4

then

cos(x/2) = -1/2, or x=+/-4pi/3 + 4kpi
or
cos(x/2) = 1, or x = 0 + 4kpi

Answer 5

This is possible only when x = 0 degree.