The sum of the solutions in (0,2π) of the equation cosxcos(π3−x)cos(π3+x)=14 is

cosxcos(π3−x)cos(π3+x)=14 14.cos3x=14 cos3x=1 3x=2nπ⇒x=2nπ3 Solutions are 0,2π3,4π3 Sum of the solutions =0+2π3+4π3=2π

The sum of the solutions in (0,2π) of the equation cosxcos(π3−x)cos(π3+x)=14 is

cosxcos(π3−x)cos(π3+x)=14 14.cos3x=14 cos3x=1 3x=2nπ⇒x=2nπ3 Solutions are 0,2π3,4π3 Sum of the solutions =0+2π3+4π3=2π

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The sum of the solutions in $(0, 2 π)$ of the equation $\cos x \cos (\frac{π}{3} - x) \cos (\frac{π}{3} + x) = \frac{1}{4}$ is

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Detailed Solution

\cos x \cos (\frac{π}{3} - x) \cos (\frac{π}{3} + x) = \frac{1}{4}

$\frac{1}{4} . \cos 3 x = \frac{1}{4}$

$\cos 3 x = 1$

$3 x = 2 n π \Rightarrow x = \frac{2 n π}{3}$

Solutions are $0, \frac{2 π}{3}, \frac{4 π}{3}$

Sum of the solutions $= 0 + \frac{2 π}{3} + \frac{4 π}{3} = 2 π$

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The sum of the solutions in (0,2π) of the equation cosxcos(π3−x)cos(π3+x)=14 is

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The sum of the solutions in $(0, 2 π)$ of the equation $\cos x \cos (\frac{π}{3} - x) \cos (\frac{π}{3} + x) = \frac{1}{4}$ is