Question

If $\sec \theta =max(x+\frac{1}{x}),x\in R,$ where $x<0$, then the value of $\theta$

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

Answer 1

The correct option is C ${120}^{\circ }$

$\sec \theta =max(x+\frac{1}{x})$

We know that,
$x+\frac{1}{x}\le -2$ when $x<0$
$\therefore max(x+\frac{1}{x})=-2\Rightarrow \sec \theta =-2\Rightarrow \theta ={120}^{\circ }$