Question

The most general solutions of $2^{1+|\cos x|+{\cos }^{2}x+|\cos x{|}^3+...\infty }=4$ are given by

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is A

$2\frac{1}{1-|\cos x|}=2^2\Rightarrow \frac{1}{1-|\cos x|}=2\Rightarrow |\cos x|=\frac{1}{2}$
$\Rightarrow \cos x=\pm \frac{1}{2}.$
$\therefore x=2n\pi \frac{\pi }{3},2n\pi \pm (\pi -\frac{\pi }{3})$
$=2n\pi \pm \frac{\pi }{3},(2n\pm 1)\pi \mp \frac{\pi }{3}=n\pi \pm \frac{\pi }{3}.$