Question

4sinxsin(π/3- x) sin (π/3+x) = sin3x
please someone tell me answer to this question​

Answer 1

Answer:

Given, 4 * sin x * sin(x + π/3) * sin(x + 2π/3)

= 4 * sin x * {sin x * cos π/3 + cos x * sin π/3} * {sin x * cos 2π/3 + cos x * sin 2π/3}

= 4 * sin x * {(sin x)/2 + (√3 * cos x)/2} * {-(sin x)/2 + (√3 *cos x)/2}

= 4 * sin x * {-(sin2 x)/4 + (3 * cos2 x)/4}

= sin x * {-sin2 x + 3 * cos2 x}

= sin x * {-sin2 x + 3 * (1 - sin2 x)}

= sin x * {-sin2 x + 3 - 3 * sin2 x}

= sin x * {3 - 4 * sin2 x}

= 3* sin x - 4sin3 x

= sin 3x

So, 4 * sin x * sin(x + π/3) * sin(x + 2π/3) = sin 3x