If $\cos 2 B=\frac{\cos (A+C)}{\cos (A-C)}$, then

$\tan A, \tan B$ and $\tan C$ are in AP

$\tan A, \tan B$ and $\tan C$ are in HP

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Analyzing +4 | -1

\cos 2 B=\frac{\cos (A+C)}{\cos (A-C)}

, then

View answer and explanation

Correct option: B

\tan A, \tan B

and

\tan C

are in GP

Option B (

\tan A, \tan B

and

\tan C

are in GP) is correct because by applying componendo and dividendo to the given equation, it can be shown that

\tan^2 B = \tan A \tan C

, which is the condition for a geometric progression.

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