Question

Prove that `1- cos(x) = 2sin^2(x/2)`?

Answer 1

Prove: `1- cos(x) = 2sin^2(x/2)`

Digress, for a moment, to the identity `cos(2u) = 1 - 2sin^2(u)`

Substitute u = x/2:

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

Add `2sin(x/2)-cos(x)` to both sides:

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

Return to the original equation and make the above substitution:

`1- cos(x) = 1-cos(x)` Q.E.D.