Let $S \subset (0, π)$ denote the set of values of x satisfying the equation $8^{1 + | c o s x | + c o s^{2} x + | c o s^{3} x | + . . . t o \infty} = 4^{3}$ .Then, S=

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Solution

The correct option is D

We know that

$- 1 \leq c o s x \leq 1$

$\Rightarrow | c o s x | \leq 1$

But,

$x \in S \Rightarrow x \in (0, π) \Rightarrow | c o s x | < 1$

Now,

$8^{1 + | c o s x | + c o s^{2} x + | c o s^{3} x | x . . . t o} = 4^{3}$

$\Rightarrow \frac{1}{1 - | c o s x |} = 2$

$\Rightarrow | c o s x | = \pm \frac{1}{2}$

$\Rightarrow | c o s x | = \pm \frac{1}{2}$

$\Rightarrow x = π / 3, 2 π / 3$

$\Rightarrow S = {π / 3, 2 π / 3}$

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