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If tan beta=2sin alpha sin gamma co sec(...

If `tan beta=2sin alpha sin gamma co sec(alpha+gamma)`, then `cot alpha,cot beta,cotgamma` are in

A

AP

B

GP

C

HP

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
A
`tan beta=22sin alpha sin gamma co sec (alpha+gamma)=(2sin alpha sin gamma)/(sin(alpha+gamma))`
or `cos beta=(sin(alpha+gamma))/(2sin alpha sin beta)`
or `2 cot beta=(sin alpha cos gamma+cos alpha sin gamma)/(sin alpha sin gamma)=cot alpha+cot gamma`
or `cot alpha,cot beta, cot gamma` are in AP.
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