Q154 / 270 · NDA 2013 (Phase 2) · Mathematics

If $\cos x=\frac{1}{3}$, then what is $\sin x \cdot \cot x \cdot \operatorname{cosec} x \cdot \tan x$ equal to?

  • A
    $\frac{2}{3}$
  • B
    $\frac{3}{2}$
  • C
    2
  • Correct answer
    D
    1

Solution

$\begin{aligned} & \cos x=\frac{1}{3} \\ & \sin x \cdot \cot x \cdot \operatorname{cosec} x \cdot \tan x \\ & =\sin x \cdot \frac{1}{\tan x} \cdot \frac{1}{\sin x} \cdot \tan x=1\end{aligned}$

Hence, the correct answer is option: 'D'.

Relevant Questions