Question

What is general solution of
$sin \alpha = cos \beta$ ?

Answer 1

Sine A  = Cos  B  = Sin (90°+ B)
    A =  π/2 + B  or  π- (π/2 +B)      principal solutions in the range    [0, 2π].

       A  = π/2 + B   or   π/2 - B
 
general solutions are :  2 n π + π/2 + B  or  2nπ + π/2 - B

Answer 2

Sine A  = Cos  B  = Sin (90°+ B)

   A =  π/2 + B  or  π- (π/2 +B)      principal solutions in the range    [0, 2π].

      A  = π/2 + B   or   π/2 - B

 

general solutions are :  2 n π + π/2 + B  or  2nπ + π/2 - B