The general solution of the equation ${sin}^{2} x + {cos}^{2} 3 x = 1$ is equal to;

x = \frac{n π}{2}

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x = n π + \frac{π}{4}

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x = \frac{n π}{4}

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x = n π + \frac{π}{2}

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Solution

The correct option is C $x = \frac{n π}{4}$
Given ${sin}^{2} x + {cos}^{2} 3 x = 1$
$⟹ {sin}^{2} x = 1 - {cos}^{2} 3 x$
$⟹ {sin}^{2} x = {sin}^{2} 3 x$
$⟹ 3 x = n π \pm x, n \in I$
$⟹ 3 x = n π + x$ or $3 x = n π - x$
$⟹ 2 x = n π$ or $4 x = n π$
$⟹ x = \frac{n π}{2}$ or $x = \frac{n π}{4}$
As $x = \frac{n π}{2}$ is also part of $x = \frac{n π}{4}$ for $n =$ even
So the general solution is $x = \frac{n π}{4}, n \in I$

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