The set of all `xin((-pi)/2,pi/2)` satisfying `|4sinx-1|

Options

A. `(- pi/10, (3pi)/10)`
B. `(pi/10, (3pi)/10)`
C. `(pi/10, (3pi)/10)`
D. none of these

Answer

A

Explanation

We have `|4 sin x-1| lt sqrt(5)`
`rArr -sqrt(5) lt 4 sin x-1 lt sqrt(5)`
or `-((sqrt(5)-1)/4) lt sin x lt ((sqrt(5)+1)/4)`
or `- "sin" pi/10 lt sin x lt "cos" pi/5`
or `sin (- pi/10) lt sin x lt sin (pi/2-pi/5)`
or `sin (- pi/10) lt sin x lt "sin" (3pi)/10`
`rArr x in (- pi/10, (3pi)/10)`