Question

Set of values of x satisfying cos^–1$\sqrt{x}$> sin^–1$\sqrt{x}$

• A. $\left( 0,\frac{1}{2} \right)$
• B. $\left\lbrack 0,\frac{1}{2} \right)$
• C. $\left( \frac{1}{2},1 \right)$
• D. $\left( \frac{1}{2},1 \right\rbrack$

Answer 1

Answer: (B)

$\left\lbrack 0,\frac{1}{2} \right)$

Answer 2

cos^–1$\sqrt{x}$ > $\frac{\pi}{2} - \cos^{- 1}\sqrt{x}$ [Q x ³ 0]

$\cos^{- 1}\sqrt{x} > \frac{\pi}{4}$

̃ $\frac{\pi}{4} < \cos^{- 1}\sqrt{x} \leq \frac{\pi}{2}$

0 £ $\sqrt{x}$ < $\frac{1}{\sqrt{2}}$

0 £ x < $\frac{1}{2}$