If `xsina+ysin2a+zsin3a=sin4a` `xsinb+ysin2b+zsin3b=sin4b`, `xsinc+ysin2c+zsin3c=sin4c`, then the roots of the equation `t^3-(z/2)t^2-((y+2)/4)t+((z-x)/8)=0,a , b , c ,!=npi,` are (a)`sina ,sinb ,sinc` (b) `cosa ,cosb ,cosc` (c)`sin2a ,sin2b ,sin2c` (d) `cos2a ,cos2bcos2c`

Options

A. `cos a, cos b, cos c`
B. `sin a, sin b, sin c`
C. `sin 2a, sin 2b, sin 2c`
D. `cos 2a, cos 2b, cos 2c`

Answer

A

Explanation

a, b, c are roots of equation.
`x sin theta+ y sin 2 theta + z sin 3 theta = sin 4 theta`
`rArr x sin theta+y (2 sin theta cos theta) + z (3 sin theta -4 sin^(3) theta)`
`= 4 sin theta cos theta cos 2 theta`
`rArr cos^(3) theta-z/2 cos^(2) theta-(y+2)/4 cos theta + (z-x)/8=0`