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Mathematics 20 Online
OpenStudy (anonymous):

True or false and why. I think it is false but I'm having trouble explaining it. cos α/2 =+/- square root of (1+cosα/2), where the + or - sign depends on the angle α/2.

OpenStudy (dumbcow):

its actually true...its a half-angle identity

OpenStudy (anonymous):

what if alpha = 0 ?

OpenStudy (anonymous):

wait is it cos(x/2) or (cosx)/2

OpenStudy (anonymous):

what dumbcow said, it is correct assuming you mean \[\cos(\frac{\alpha}{2})=\pm\sqrt{\frac{1+\cos(\alpha)}{2}}\]

OpenStudy (anonymous):

yes that is correct

OpenStudy (anonymous):

yus that is true. sorry the lack of brackets confused me

OpenStudy (anonymous):

then it is right \(\alpha =0\) poses no challenge to the formula, get 1 on both sides

OpenStudy (dumbcow):

the why comes from using double angle identity \[\cos(2 \alpha) = 2\cos^{2} \alpha -1\] solve for cos(alpha) and you obtain the half angle identity

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