Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$-\sqrt{5}<4sinx-1<\sqrt{5}$

$\Rightarrow$ $\left(\frac{\sqrt{5}-1}{4}\right)<sinx<\frac{\sqrt{5}+1}{4}$

$\Rightarrow$ $-sin\frac{\pi }{10}<sinx<cos\frac{\pi }{5}$

$\Rightarrow$ $sin\left(\frac{-\pi }{4}\right)$ < sinx < $sin(\frac{\pi }{4}-\frac{\pi }{5})$

$\Rightarrow$ $sin\left(\frac{-\pi }{4}\right)<sinx<sin\frac{3\pi }{10}$

$\Rightarrow$ $x\in (\frac{-\pi }{4},\frac{3\pi }{10})$