Question

If $a+\frac{\pi }{2}<2{\tan }^{-1}x+3{\cot }^{-1}x<b$ then 'a' and 'b' are respectively.

• A. 0 and 2$\pi$
• B. 0 and $\pi$
• C. $\frac{-\pi }{2}$ and $\frac{\pi }{2}$
• D. $\frac{\pi }{2}$ and $2\pi$

Answer 1

Answer: (D)

$a+\frac{\pi }{2}<si{n}^{-1}x+2co{t}^{-1}x+\frac{\pi }{2}<b$
$a+\frac{\pi }{2}<\frac{\pi }{2}+co{t}^{-1}x+\frac{\pi }{2}<b$
$a+\frac{\pi }{2}<\pi +co{t}^{-1}x<b$
$a-\frac{\pi }{2}<co{t}^{-1}x<b-\pi$
$\left[since0<co{t}^{1}x<\pi \right]$
$\Rightarrow a=\frac{\pi }{2}b=2\pi$