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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`sina ,sinb ,sinc`(b) `cosa ,cosb ,cosc``sin2a ,sin2b ,sin2c`(d) `cos2a ,cos2bcos2c`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` |
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Answer» Correct Answer - A 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` |
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