Question

The set of all x in $(-\pi ,\pi )$ satisfying
$|4\sin x-1|<\sqrt{5}$ is given by

• A. $(-\frac{\pi }{10},\frac{3\pi }{10})$
• B. $(-\frac{\pi }{10},\pi )$
• C. $(-\pi ,\pi )$
• D. $(-\pi ,\frac{3\pi }{10})$

Answer 1

The correct option is A $(-\frac{\pi }{10},\frac{3\pi }{10})$

$-5^{0.5}<4\sin x-1<5^{0.5}$
$\frac{1-5^{0.5}}{4}<\sin x<\frac{5^{0.5}+1}{4}$
$x$ lies in the interval, ($\frac{-\pi }{10},\frac{3\pi }{10})$
Hence, option 'A' is correct.