Question

If $co{s}^{-1}x>si{n}^{-1}x$, then

• A. $\frac{1}{\sqrt{2}}<x\le 1$
• B. $0\le x<\frac{1}{\sqrt{2}}$
• C. $-1\le x<\frac{1}{\sqrt{2}}$
• D. $x>0$

Answer 1

Answer: (C)

$co{s}^{-1}x>si{n}^{-1}x$
$\Rightarrow \frac{\pi }{2}-si{n}^{-1}x>si{n}^{-1}x$
$\Rightarrow \frac{\pi }{2}>2si{n}^{-1}x$
$\Rightarrow si{n}^{-1}x<\frac{\pi }{4}$
$\Rightarrow x<sin\frac{\pi }{4}$
$\Rightarrow x<\frac{1}{\sqrt{2}}$