Question

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

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is A

$1+\left|\cos x\right|+{\cos }^{2}x..........$
$=\frac{1}{1-\left|\cos x\right|}$
$\Rightarrow \frac{1}{8^{1-\left|\cos x\right|}=4^3}$ $\Rightarrow 2^{\frac{3}{1-\left|\cos x\right|}}=2^6\Rightarrow \frac{3}{1-\left|\cos x\right|}=6\Rightarrow 1-\left|\cos x\right|=\frac{1}{2}$
$\left|\cos x\right|=\frac{1}{2}\Rightarrow \cos x=\pm \frac{1}{2}$
$\cos x=\frac{1}{2}$ will give least positive value of x $x=\frac{\pi }{3}$Ans.