jika sin (A - π /4) - 5cos (A- π /4) = 0 maka tan A =..

sin (A - π /4) - 5cos (A- π /4) = 0

sin(A - π /4) = -cos(A)*sin(π /4) + sin(A)*cos(π /4)
                    = -cos(A)*√2/2 + sin(A)*√2/2
                    = -(√2/2)cos(A) + (√2/2)sin(A)

cos(A - π /4) = cos(A)*cos(π /4) + sin(A)*sin(π /4)
                    = cos(A)*√2/2 + sin(A)*√2/2
                    = (√2/2)cos(A) + (√2/2)sin(A)

(√2/2)cos(A) = (√2.cos(A))/2
                     = (2^(1/2).cos(A))/2
                     = cos(A)/2^(1/2)
                     = cos(A)/√2

(√2/2)sin(A) = (√2.sin(A))/2
                     = (2^(1/2).sin(A))/2
                     = sin(A)/2^(1/2)
                     = sin(A)/√2

= cos(A)/√2 + sin(A)/√2
= (cos(A) + sin(A))/√2

= 5.((√2/2)cos(A) + (√2/2)sin(A))
= 5.((cos(A)/√2)+(sin(A)/√2)
= 5.((cos(A)+(sin(A))/√2)

= sin (A - π /4) - 5cos (A- π /4)
= -(√2/2)cos(A) + (√2/2)sin(A) -5((√2/2)cos(A) + (√2/2)sin(A))
= -((cos(A)+sin(A))/√2) - 5.((cos(A)+(sin(A))/√2)
= -((cos(A)+sin(A)) - 5.(cos(A)+(sin(A)))/√2
= (-4sin(A)-6cos(A))/√2
= -2(2sin(A)-3cos(A))/√2 
= -√2(2sin(A)-3cos(A))

-√2(2sin(A)-3cos(A)) = 0
-√2(2sin(A)-3cos(A))/cos(A) = 0/cos(A)
(-2√2sin(A))/cos(A))-3√2 = 0
(-√2(2tan(A) + 3) = 0
(-√2(2tan(A) + 3)/-√2 = 0/-√2
2tan(A) + 3 = 0
      2tan(A) = -3
        tan(A) = -3/2