Question

The least positive values of $x$ satisfy the equation $8^{1+|\cos x|+{\cos }^{2}x+|{\cos }^{3}x|+\dots \dots \infty }=4^3$ 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)

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