Question

Evaluate ${\sec }^{-1}\left(\sec \right(-{30}^{°}\left)\right)$$=$

• A. $-60°$
• B. $-30°$
• C. $30°$
• D. $150°$

Answer 1

The correct option is C

$30°$

Solve the function:

We know, $\sec \left(-\varnothing \right)=\sec \varnothing$

Then, $\sec \left(-30°\right)=\sec 30°$

Now, ${\sec }^{-1}\left(\sec \varnothing \right)=\varnothing$

Then, ${\text{sec}}^{-1}\left(\sec 30°\right)=30°$

Hence, the correct answer is option (c).