Question

For any angle $\theta \in [0,\pi ],\text{cosec}\theta =1,$ then $\sec \frac{\theta }{2}=$

• A. $\sqrt{2}$
• B. $2$
• C. $1$

Answer 1

The correct option is A $\sqrt{2}$

Given $\theta \in [0,\pi ],\text{cosec}\theta =1$
We know $\text{cosec}\theta =1\text{for}\theta =\frac{\pi }{2},\frac{5\pi }{2},...$
Since, $\theta \in [0,\pi ],\text{cosec}\theta =1\Rightarrow \theta =\frac{\pi }{2}$

$\therefore \sec \frac{\theta }{2}=\sec \frac{\pi }{4}=\sqrt{2}$