cos2A=1-2(sinA)^2 therfor
the equation becomes
2(1-2(sinA)^2)+1+sinA=0
2-4(sinA)^2+1+sinA=0
4(sinA)^2-sinA-3=0
this is a quadratic equation.solving this we get
sinA=1 or sinA=-3/4
1)sinA=1
A=pi/2
2)sinA=-3/4
let sinB=3/4(NOT -3/4)
SO B=arcsin3/4
so
A=pi+B,2pi-B