Question

The least positive values of $x$ satisfy the equation $8^{1+|\cos x|+\cos ^2 x+\left|\cos ^3 x\right|+\ldots \ldots \infty}=4^3$ will be (where $|\cos x |<1$ )

• A. $\frac{\pi}{3}$
• B. $\frac{2 \pi}{3}$
• C. $\frac{\pi}{4}$
• D. $\frac{3 \pi}{4}$

Answer 1

Answer: (A)

$ 8^{\frac{1}{1-|\cos x|}}=4^3 $
$2^{\frac{3}{1-|\cos x|}}=2^6 $
$\frac{3}{1-|\cos x|}=6$
$3=6-6|\cos x|$
$6|\cos x|=3 $
$|\cos x|=\frac{1}{2} $
$x=\frac{\pi}{3} \text { (least posit }$