1.

If `x sintheta=ysin(theta+(2pi)/(3))=z sin(theta+(4pi)/(3)),` thenA. `x+y+z=0`B. `xy+yz+zx=0`C. `xyz+x+y+z=1`D. none of these

Answer» Correct Answer - B
We have,
`x sintheta=y sin(theta+(2pi)/(3))=zsin(theta+(4pi)/(3))`
`implies(sin theta)/(1/x)=(sin (theta+(2pi)/(3)))/(1/y)=(sin(theta+(4pi)/(3)))/(1/z)`
`=(sintheta)/(1/x)=(sin(theta+(2pi)/(3)))/(1/y)=(sin(theta+(4pi)/(3)))/(1/z)`
`=(sin theta+sin(theta+(2pi)/(3))+sin(theta+(4pi)/(3)))/(1/x+1/y+1/z)`
`implies(sintheta)/(1/x)=(sin(theta+(2pi)/(3)))/(1/y)=(sin(theta+(4pi)/(3)))/(1/z)`
`implies(sintheta)/(1/x)xx((1)/(x)+(1)/(y)+(1)/(z))=0`
`implies1/x+1/y+1/z=0impliesxy+yz+zx=0`


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