The solution(s) of the equation $cos 2 x sin 6 x = cos 3 x sin 5 x$ in the interval $[0, π]$ is/are

\frac{π}{6}

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\frac{π}{2}

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\frac{2 π}{3}

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\frac{5 π}{6}

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Solution

The correct options are
A $\frac{π}{6}$
B $\frac{π}{2}$
D $\frac{5 π}{6}$
$cos 2 x sin 6 x = cos 3 x sin 5 x \Rightarrow 2 cos 2 x sin 6 x = 2 cos 3 x sin 5 x \Rightarrow sin 8 x - sin (- 4 x) = sin 8 x - sin (- 2 x) \Rightarrow sin 8 x + sin 4 x = sin 8 x + sin 2 x \Rightarrow sin 4 x - sin 2 x = 0 \Rightarrow 2 sin 2 x cos 2 x - sin 2 x = 0 \Rightarrow sin 2 x (2 cos 2 x - 1) = 0$
$\Rightarrow sin 2 x = 0$ or $cos 2 x = \frac{1}{2}$
$\Rightarrow 2 x = n π$ or $2 x = 2 n π \pm \frac{π}{3}$
For $x ϵ [0, π]$
$x = 0, \frac{π}{2}, \frac{π}{6}, \frac{5 π}{6}$

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The solution(s) of the equation cos2xsin6x=cos3xsin5x in the interval [0,π] is/are

The correct options are A π6 B π2 D 5π6cos2xsin6x=cos3xsin5x⇒2cos2xsin6x=2cos3xsin5x⇒sin8x−sin(−4x)=sin8x−sin(−2x)⇒sin8x+sin4x=sin8x+sin2x⇒sin4x−sin2x=0⇒2sin2xcos2x−sin2x=0⇒sin2x(2cos2x−1)=0⇒sin2x=0 or cos2x=12⇒2x=nπ or 2x=2nπ±π3For xϵ[0,π]x=0,π2,π6,5π6

The solution(s) of the equation $cos 2 x sin 6 x = cos 3 x sin 5 x$ in the interval $[0, π]$ is/are