Question

if 3 sinx + 4 cosx = 5 show that
3 cosx - 4 sinx = 0

Answer 1

hey friend
here is your answer
ANS    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

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