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If 2 sin alpha cos beta sin gamma=sin b...

If ` 2 sin alpha cos beta sin gamma=sin beta sin( alpha-gamma)`. Then, show `tan alpha, tan beta` and `tan gamma` are in harmonic progression.

A

A.P.

B

G.P.

C

H.P.

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`2 sin alpha cos beta sin gamma=sinbeta sin(alpha+gamma)`
`implies2sinalpha cos betasingamma=sinalphasinbetacosgamma+cosalpha sinbetasingamma`
`implies2 cot alpha, cot beta, cot gamma` are in A.P.
`impliestan alpha, beta,tangamma` are in H.P.
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