Question

If $\sec ^ { 2 } \theta = \frac { 4 } { 3 }$ then the general value of $\theta$ is

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

Answer 1

Answer: (B)

$n \pi \pm \frac { \pi } { 6 }$

Answer 2

$\sec ^ { 2 } \theta = \frac { 4 } { 3 }$ $\Rightarrow \cos ^ { 2 } \theta = \frac { 3 } { 4 } = \left( \frac { \sqrt { 3 } } { 2 } \right) ^ { 2 }$ $\Rightarrow \cos ^ { 2 } \theta = \cos ^ { 2 } \frac { \pi } { 6 }$

$\therefore \theta = n \pi \pm \frac { \pi } { 6 }$ .