Question

Find the most general solution of $2^{1+\left|\cos x\right|+{\cos }^{2}x+{\left|\cos x\right|}^3+...\infty }=4$

• A. $x=n\pi \pm \frac{\pi }{9}$, $n\in Z$
• B. $x=n\pi \pm \frac{\pi }{6}$, $n\in Z$
• C. $x=n\pi \pm \frac{\pi }{12}$, $n\in Z$
• D. $x=n\pi \pm \frac{\pi }{3}$, $n\in Z$

Answer 1

The correct option is D $x=n\pi \pm \frac{\pi }{3}$, $n\in Z$

We have $2^{1+\left|\cos x\right|+{\cos }^{2}x+{\left|\cos x\right|}^3+...\infty }=4$

$2^{1+\left|\cos x\right|+{\left|\cos x\right|}^2+{\left|\cos x\right|}^3+...\infty }=4$

$2^{\frac{1}{1-\left|\cos x\right|}}=2^2$

$1-\left|\cos x\right|=\frac{1}{2}$

$\left|\cos x\right|=\frac{1}{2}$ or $\cos x=\pm \frac{1}{2}$

$\Rightarrow$ $x=n\pi \pm \frac{\pi }{3}$, $nϵZ$