Question

If $\frac { 1 - \cos 2 \theta } { 1 + \cos 2 \theta } = 3$then the general value of $\theta$ is

• A. $2 n \pi \pm \frac { \pi } { 6 }$
• B. $n \pi \pm \frac { \pi } { 6 }$
• C. $2 n \pi + \frac { \pi } { 3 }$
• D. $n \pi \pm \frac { \pi } { 3 }$

Answer 1

Answer: (D)

$n \pi \pm \frac { \pi } { 3 }$

Answer 2

$\frac { 1 - \cos 2 \theta } { 1 + \cos 2 \theta } = 3$ $\Rightarrow \frac { 2 \sin ^ { 2 } \theta } { 2 \cos ^ { 2 } \theta } = 3 \Rightarrow \tan ^ { 2 } \theta = 3 = ( \sqrt { 3 } ) ^ { 2 } \Rightarrow \tan ^ { 2 } \theta = \tan ^ { 2 } \frac { \pi } { 3 }$ $\theta = n \pi \pm \frac { \pi } { 3 }$.