Question

If $\frac{1-cos2\theta }{1+cos2\theta }=3$ then the general solution of $\theta$ is

• A. $2n\pi \pm \pi /6,n\in I$
• B. $n\pi \pm \pi /6,n\in I$
• C. $2n\pi \pm \pi /3,n\in I$
• D. $n\pi \pm \pi /3,n\in I$

Answer 1

The correct option is D $n\pi \pm \pi /3,n\in I$

$\frac{1-cos2\theta }{1+cos2\theta }=3$
$\Rightarrow \frac{2si{n}^2\theta }{2co{s}^2\theta }=3$
$\Rightarrow ta{n}^2\theta =3=(\sqrt{3}{)}^2$
$\Rightarrow ta{n}^2\theta =ta{n}^2\frac{\pi }{3}$
So, the general solution is
$\theta =n\pi \pm \frac{\pi }{3},n\in I$