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If cos 2B =cos(A+C)/cos( A-C), then tanA...

If `cos 2B =cos(A+C)/cos( A-C)`, then `tanA, tanB, tanC` are in

A

AP

B

GP

C

HP

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`cos2B=(cos(A+C))/(cos(A-C))=(cosAcosC-sinAsinC)/(cosAcosC+sinAsinc)`
`rArr(1-tan^(2)B)/(1+tan^(2)B)=(1-tanAtanC)/(1+tanAtanC)`
`rArr1+tan^(2)B-tanAtanC-tanCtan^(2)B`
`=1-tan^(2)B+tanAtanC-tanAtanCtan^(2)B`
`rArr2tan^(2)B=2tanAtanC`.
`rArrtan^(2)B=tanAtanC`
Hence ,tan A,tan B and tan C will be in GP
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