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If $Tan 8 A - Tan 5 A - Tan 3 A = K Tan 8 A Tan 5 A . Tan 3 A$ then $k =$

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answer is A.

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Detailed Solution

$\tan 8 A - \tan 5 A - \tan 5 A - \tan 3 A = k \tan 8 A \tan 5 A \tan 3 A \tan 8 A = \tan (5 A + 3 A) \tan 8 A = \frac{\tan 5 A + \tan 3 A}{1 - \tan 5 A \tan 3 A} \tan 8 A - \tan 5 A - \tan 3 A = \tan 8 A \tan 5 A \tan 3 A k = 1$

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