Question

Prove that `2sin(A/2)=+-sqrt(1+sinA) +-sqrt(1-sinA)`?

Answer 1

See below.

Explanation:

`(sqrt(1+sinA) -sqrt(1-sinA))^2=1+sinA+1-sinA-2sqrt(1-sin^2A) =`

`= 2-2cosA =`

`= 2(1-cosA)=2(1-(1-2sin^2(A/2)))=4sin^2(A/2)`

and hence `sqrt(1+sinA)-sqrt(1-sinA)=2sin(A/2)`