Question

if cos 2B=cos(A+C)/cos(A-C) then TanA, TanB, TanC are in​

Answer 1

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Answer 2

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Step-by-step explanation:

cos2B=cos(A−C)cos(A+C)

Using componendo-dividendo

cos2B−1cos2B+1=cos(A+C)

−cos(A−C)cos(A+C)+cos(A−C)

1−2sin2B−12cos2B−1+1=cosAcosC−

sinAsinC−cosAcosC−si

nAsinCcosAcosC−sinAsinC+cosA

cosC+sinAsinC

−cot2B=−cotAcotC

tan2B=tanAtanC

Hence tanA,tanB,tanC are in G.P