Question

The value of 4 × sin x × sin(x + π/3) × sin(x + 2π/3) is

Answer 1

Answer:

cos (5pi) = cos (pi + 4pi) = cos pi = - 1

Answer 2

Step-by-step explanation:

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

Answered on: 2017/09/04 by ExamFear Share on Facebook Share of TwitterReport Abuse

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