The least positive root of the equation $cos 3 x + sin 5 x = 0$ is

\frac{π}{12}

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\frac{π}{16}

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\frac{3 π}{16}

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\frac{3 π}{4}

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Solution

The correct option is D $\frac{3 π}{16}$
$cos 3 x + sin 5 x = 0$
$\Rightarrow sin (\frac{π}{2} - 3 x) = - sin 5 x$
$\Rightarrow sin (\frac{π}{2} - 3 x) = sin (- 5 x)$
The general solution of the above equation is
$\frac{π}{2} - 3 x = n π + (- 1)^{n} (- 5 x)$
$\Rightarrow (- 1)^{n} 5 x - 3 x = π (n - \frac{1}{2})$
For $n = - 1$ , we get the least positive value of $x$ as $x = \frac{3 π}{16}$

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