Question

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