Within what limits must `A/2` lie if `2sin(A/2)=sqrt(1+sinA)-sqrt(1-sinA)`

Explanation

Clearly, `sinA/2 + cosA/2 =-sqrt(1+sinA)` for `2npi-(5pi)/(4) lt A/2 lt 2npi-pi/4` …………(i)
`sinA/2-cosA/2=-sqrt(1-sinA)` for `2npi-(3pi)/4 lt A/2 lt 2npi +pi/4` …………(ii)
For both (i) and (ii) to be true
`2npi - (3pi)/4 lt A/2 lt 2npi -pi/4`