One of the solution of the equation ` 8 sin^(3) theta-7 sin theta+sqrt(3) cos theta=0` lies in the interval

Options

A. `(0,10^(@)]`
B. `(10^(@),20^(@)]`
C. `(20^(@),30^(@)]`
D. `(30^(@),40^(@)]`

Answer

B

Explanation

`6 sin theta -2 sin 3theta -7 sin theta +sqrt(3) cos theta=0`
`sqrt(3) cos theta- sin theta= 2 sin 3 theta`
It can be written as
`2( sin (60^(@)- theta))=2 sin 3 theta`
` sin (60^(@)-theta)= sin 3 theta`
`60^(@)=4 theta`
`implies theta = 15^(@)` is one of the value.