Sum of solutions in x ∈ (0,4π ) of the equation 4sin frac{x}{3}left( {sin left( {frac{

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Trigonometrical Equations

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The sum of the solutions in $x \in (0,4\pi )$ of the equation $4\sin \frac{x}{3}\left( {\sin \left( {\frac{{\pi + x}}{3}} \right)} \right)\sin \left( {\frac{{2\pi + x}}{3}} \right) = 1$ is

A

$6\pi $

B

$4\pi $

C

$3\pi $

D

None of these

Solution

$4\left(\frac{\sin x}{4}\right)=1$

$\sin x=\frac{4}{4}=1$

$\therefore $ sum of solutions $=3 \pi$

Standard 11

Mathematics

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