The general value of $x$ for the equation $9^{cos x} - {2.3}^{cos x} + 1 = 0$

n π

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\frac{n π}{2}

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2 n π

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(2 n + 1) \frac{π}{2}

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Solution

The correct option is D $(2 n + 1) \frac{π}{2}$
take $3^{cos x} = t$
we get
$t^{2} - 2 t + 1 = 0$
$t = 1$
so $3^{cos x} = 1$
$∴ cos x = 0$
$x = (2 n + 1) \frac{π}{2}$

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