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If alpha and beta are non-zero real numb...

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

`tan ((alpha )/(2)) + sqrt3 tan ((beta)/(2)) =0`

B

`sqrt3 tan ((alpha)/(2)) + tan ((beta)/(2)) =0`

C

`tan ((alpha )/(2)) - sqrt3 tan ((beta)/(2)) =0`

D

`sqrt3 tan (( alpha )/(2)) - tan ((beta)/(2))= 0`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`cos beta ( 2+ cos alpha ) = 1+ 2 cos alpha `
`rArr (cos beta)/(1) = (1+2 cos alpha )/(2 + cos alpha )`
`rArr (1-cos beta)/(1+cos beta) = (1-cos alpha )/(3(1+cos alpha ))`
`rArr tan ^(2) ""(alpha )/(2) = 3 tan ^(2) ""(beta)/(2)`
`rArr tan ""(alpha )/(2) = pm sqrt3 tan ""(beta)/(2)`
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