Question

Number of distinct roots of D =$\left| \begin{matrix} \tan x & \cot x & \cot x \\ \cot x & \tan x & \cot x \\ \cot x & \cot x & \tan x \end{matrix} \right|$ = 0

in the interval $\left\lbrack - \frac{\pi}{4},\frac{\pi}{4} \right\rbrack$ is

• A. 0
• B. 2
• C. 1
• D. 3

Answer 1

Answer: (B)

2

Answer 2

D = (tan x + 2 cot x) $\left| \begin{matrix} 1 & \cot x & \cot x \\ 1 & \tan x & \cot x \\ 1 & \cot x & \tan x \end{matrix} \right|$ = 0

or (tan x + 2 cot x) (tan x – cot x)² = 0