Question

solve 4sinxsin2xsin4x = sin3x

Answer 1

sin 3x = 4 sinx sin2x sin4x
=> sin 3x = 2 sinx (2 sin 2x sin 4x)
=> sin 3x = 2 sinx {cos (2x-4x) - cos (2x+4x)}
=> sin 3x = 2 sinx (cos 2x - cos 6x)
=> sin 3x = 2 sinx cos 2x - 2 sin x cos 6x
=> sin 3x = {sin (x+2x) + sin (x-2x)} - {sin (x+6x) + sin (x-6x)}
=> sin 3x = sin 3x + sin (-x) - sin 7x - sin (-5x)
=> sin x + sin 7x + sin 5x = 0

Answer 2

4sinxsin2xsin4x=sin3x

4sinxsin4xsin2x=sin3x

2.2sinxsin4xsin2x=sin 3x

2.(2sinxsin4x)sin2x=sin3x

2.(cos3x-cos5x)sin2x=sin3x.

( Using 2sinasinb formula)

2cos3xsin3x-2cos5xsin2x=sin3x

sin5x-sinx-sin7x+sin3x=sin3x

Sin5x-sinx-sin7x=sin3x-sin3x

Sin5x-sinx-sin7x=0

Sin5x--sin7x=sinx

2cos6xsinx=sinx.

(sinx=0

x=nπ)

2cos6x=-1

Cos6x=-1/2

6x=2nπ+/-2π/3

x=nπ/3+/-π/9