The equation $3^{sin 2 x + 2 {cos}^{2} x} + 3^{1 - sin 2 x + 2 {sin}^{2} x} = 28$ is satisfied
for the values of x given by :

cos x = 0

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sin x = - 1

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tan x = 1

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sin x = \frac{1}{2}

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Solution

The correct option is B $cos x = 0$
we get
$3^{sin 2 x + 2 cos 2 x} + 3^{3 - (sin 2 x + 2 {cos}^{2} x)} = 28$
take $3^{sin 2 x + 2 cos 2 x} = t$
so $t + \frac{27}{t} = 28$
this gives t $= 1$
so $3^{sin 2 x + 2 cos 2 x} = 1$
so $sin 2 x + 2 cos 2 x = 0$
so $cos x = 0$

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