If `alpha and beta` are non-zero real number such that `2(cos beta-cos alpha)+cos alpha cos beta=1.` Then which of the following is treu?A. `sqrt(3) tan ((alpha)/(2))-tan((beta)/(2))=0`B. `tan((alpha)/(2)) - sqrt(3) tan((beta)/(2)) = 0`C. `tan((alpha)/(2)) + sqrt(3)((beta)/(2))=0`D. `sqrt(3) tan((alpha)/(2))+ tan((beta)/(2))=0`

If `alpha and beta` are non-zero real number such that `2(cos beta-cos

1.	If `alpha and beta` are non-zero real number such that `2(cos beta-cos alpha)+cos alpha cos beta=1.` Then which of the following is treu?A. `sqrt(3) tan ((alpha)/(2))-tan((beta)/(2))=0`B. `tan((alpha)/(2)) - sqrt(3) tan((beta)/(2)) = 0`C. `tan((alpha)/(2)) + sqrt(3)((beta)/(2))=0`D. `sqrt(3) tan((alpha)/(2))+ tan((beta)/(2))=0`
Answer» Correct Answer - B::C We have, `2(cos beta - cos alpha)+ cos alpha cos beta = 1` or `4(cos beta - cos alpha) + 2 cos alpha cos beta = 2` `rArr 1-cos alpha + cos beta - cos alpha cos beta = 2` `= 3+3 cos alpha - 3 cos beta - 3cos alpha cos beta` `rArr (1-cos alpha) (1+ cos beta)=3(1+cos alpha) (1-cos beta)` `rArr ((1-cos alpha))/((1+cos alpha)) = (3(1-cos beta))(1+cos beta))` `rArr tan^(2) (alpha)/(2) = 3 tan^(2)(beta)/(2)` `therefore tan.(alpha)/(2) pm sqrt(3) tan.(beta)/(2) =0`