Question

If $\sec \theta =min(a^x+\frac{1}{a^x}),$ where $a>0,x\in R,$ then the value of $\theta$

• A. ${120}^{\circ }$
• B. ${30}^{\circ }$
• C. ${60}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is C ${60}^{\circ }$

$\sec \theta =min(a^x+\frac{1}{a^x})$

We know that,
$a^x+\frac{1}{a^x}\ge 2$ when $a>0$
$\therefore min(a^x+\frac{1}{a^x})=2\Rightarrow \sec \theta =2\Rightarrow \theta ={60}^{\circ }$