Question

If $\cos \alpha =x+\frac{1}{x},x\in R-\left\{0\right\}$, then $\alpha \in$

• A. $(0,\frac{\pi }{2})$
• B. $(\frac{\pi }{2},\pi )$
• C. $\left\{\frac{\pi }{2}\right\}$
• D. $\varphi$

Answer 1

The correct option is D $\varphi$

$\cos \alpha =x+\frac{1}{x}$
As we know that
$x+\frac{1}{x}\in (-\infty ,-2]\cup [2,\infty )$
And $\cos \alpha \in [-1,1]$
$\Rightarrow \cos \alpha \ne x+\frac{1}{x}$ for $x\in R-\left\{0\right\}$

Therefore, $\alpha \in \varphi$