Question

The number of values of x lying in the interval (-$\pi$, $\pi$) which satisfy the equation

$8^{1+|cosx|+|co{s}^{2}x|+...............+\infty }$=64 is

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is B

4

1 + |cosx| + $co{s}^{2}x$ + |$co{s}^{3}x$| + ............$\infty$ = $\frac{1}{1-|cosx|}$

$\frac{1}{8^{1-|cosx|}}$ = $4^3$ ⇒ $\frac{3}{1-|cosx|}$ = 6

1 = 2 - 2|cosx| ⇒ |cosx| = $\frac{1}{2}$ ⇒ |cosx| = ± $\frac{1}{2}$

x = $\frac{\pi }{3}$, $\frac{-\pi }{3}$, $\frac{2\pi }{3}$, $\frac{-2\pi }{3}$ ⇒ 4solutions