If (acosA - bsinA) = c , prove that (asinA + bcosA) = + or - (a2 + b2 - c2 )1/2

squaring on both the sides and taking theta as A,we
get-

a2cos2A + b2sin2A - 2ab sinAcosA =
c2

hence, 2absinAcosA= a2cos2A + b2sin2A-c2   
.............................................(1)

now,
asinA+bcosA=(asinA+bcosA)^2*12

                                   
=(a2sin2A+b2cos2A+2ab sinA
cosA)12

                                    
=(a2sin2A+b2cos2A+ a2cos2A + b2sin2A-
c2)12

                                     =(a2sin2A +
a2cos2A+b2cos2A + b2sin2A-
c2)12

                                     =[a2(sin2A+cos2A)+b2(sin2A+cos2A)-
c2]12

                                     as sin2A+cos2A =
1

                          asinA + bcosA = +_ ( a2 + b2 -
c2)1/2