The value of x in `(0,(pi)/(2))` satisfying the equation sin x cos x `=(1)/(4)` are . . .

Options

A. `pi/6,pi/12`
B. `pi/12,(5pi)/12`
C. `pi/8,(3pi)/8`
D. `pi/8,pi/4`

Answer

B

Explanation

We have, sinxcosx`=1/4`
`rArr2sinxcosx=1/2`
`rArrsin2x=1/2`
`rArr2x=sin^(-1)(1/2)=pi/6`
`rArrx=pi/12`
If `xin(0,pi/2),` then `x=pi/12,pi/2-pi/12=pi/12,(5pi)/12`