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. $\pi$
• E. $\frac{\pi}{6}$

Answer 1

Answer: (B)

Given, $\frac{\sin x}{\cos x} \times \frac{\sec x}{\operatorname{cosec} x} \times \frac{\tan x}{\cot x}=9$
$\Rightarrow \tan x \times \tan x \times \tan ^{2} x=9$
$\Rightarrow \tan ^{4} x=(\sqrt{3})^{4}$
$\Rightarrow \tan x=\sqrt{3}$
$\Rightarrow x=\frac{\pi}{3}$