1. ## Trig Proof Help

Hi

I have the task of constructing a proof that shows how sinx/2 can be equal to plus or minus root((1-cosx)/2). Also how cosx/2 = plus or minus root((1+cosx)/2). I've been given the hint that it would involve the fact that sinx = plus or minus root((1-cos2x)/2) and cos2x = 1-2sin^2x. Any help I could get would be appreciated.

Edit: Here is a slight clarification if I typed poorly.

Proofs for:

and

2. Hello, Kolbeck10!

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:
. . [1] sin(x/2) = ± sqrt[(1 - cos x)/2]
. . [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).