Question

Statement 1 : $si{n}^{-1}\left(\frac{1}{\sqrt{e}}\right)>ta{n}^{-1}\left(\frac{1}{\sqrt{\pi }}\right)$
Statement 2 : $si{n}^{-1}x>ta{n}^{-1}y$ for $x>y,\forall x,y\in \left(0,1\right)$

• A. Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
• B. Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
• C. Statement -1 is false, Statement-2 is true
• D. Statement -1 is true, Statement-2 is false

Answer 1

Answer: (A)

$si{n}^{-1}x=ta{n}^{-1}\frac{x}{\sqrt{1-x^2}}>ta{n}^{-1}x>ta{n}^{-1}y$
$\therefore$ statement-2 is true
$e<\pi$
$\frac{1}{\sqrt{e}}>\frac{1}{\sqrt{\pi }}$
by statement-2.
$si{n}^{-1}\left(\frac{1}{\sqrt{e}}\right)>ta{n}^{-1}\left(\frac{1}{\sqrt{e}}\right)>ta{n}^{-1}\left(\frac{1}{\sqrt{\pi }}\right)$
statement-1 is true