Question

If $\frac{\sin x}{\cos x} \times \frac{\sec x}{\operatorname{cosec} x} \times \frac{\tan x}{\cot x}=9$, where $x \in\left(0, \frac{\pi}{2}\right)$, then the value of $x$ is equal to

• A. $\frac{\pi}{4}$
• B. $\frac{\pi}{3}$
• C. $\frac{\pi}{2}$
• D. $\pi$

Answer 1

Answer: (B)

$\frac{\sin x}{\cos x} \times \frac{\sec x}{\operatorname{cosec} x} \times \frac{\tan x}{\cot x}=9$
$\Rightarrow \tan x \times \tan x \times \frac{\tan x}{\cot x}=9 \Rightarrow \tan ^{4} x=9$
$\Rightarrow \tan x=\pm \sqrt{3} \Rightarrow x=\frac{\pi}{3}$ as $x \in\left(0, \frac{\pi}{2}\right)$