The problem is strangely worded . . .
I'm not sure exactly how we should construct the proofs.
I have the task of constructing a proof that:
. .  sin(x/2) = ± sqrt[(1 - cos x)/2]
. .  cos(x/2) = ± sqrt[(1 + cos x)/2]
I've been given the hint that it would involve the fact that:
. . (a) sin x .= .± sqrt[(1 - cos2x)/2] .and
. . (b) cos2x .= .1 - 2sin²x
They actually gave us hint (a) ??
Just replace x with x/2
. . and we have: .sin(x/2) .= .± sqrt[(1 - cos x)/2] . . . . wow, that was hard!
I don't know why they gave us hint (b).
. . It's the same as hint (a).