Question

If $cot\left(\frac{\pi }{3}cos2\pi x\right)=\sqrt{3}$ , then the general solution of the equation is

• A. $x=n\pm \frac{1}{2},\left(n\in I\right)$
• B. $x=n\pm \frac{1}{3},\left(n\in I\right)$
• C. $x=n\pm \frac{1}{6},\left(n\in I\right)$
• D. $x=n\pm \frac{1}{4},\left(n\in I\right)$

Answer 1

Answer: (C)

$\frac{\pi }{3}cos\left(2\pi x\right)=n\pi +\frac{\pi }{6},n\in I$
it is true for $n=0$
$\Rightarrow \frac{\pi }{3}\cdot cos\left(2\pi x\right)=\frac{\pi }{6}\Rightarrow cos\left(2\pi x\right)=\frac{1}{2}$
$\Rightarrow 2\pi x=2n\pi \pm \frac{\pi }{3}\Rightarrow x=n\pm \frac{1}{6},n\in I$