Question

3 sinx + 4 cosx = 5

Answer 1

3sinx+4cosx=5
     => 3/5 sinx +4/5 cosx = 1
     let cosA=3/5   => sinA=4/5
     =>  cosAsinx + sinAcosx = 1
     =>  sin(x+A) = 1
Now,
       4sinx - 3cosx
  =   5(4/5sinx - 3/5 cosx)     [multipying numerator and denominator by 5]
  =   5(sinAsinx - cosAcosx)
  =   -5{cos(x+A)} = -5[root{1-(sin(x+A)^2)}] = -5 x 0 = 0          Ans 0
 
TRICK: if asinx+bcosx is given then multiply numerator and denominator by root(a^2 +b^2)
            this method is useful  in many questions