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 Question from nazz, a student: prove; tan inverse 1/4=1/3 cot inverse 52/47

You do not say what tools you have available. I would set $A = \tan^{-1} 1/4$, and then rewrite your equation as

$\tan (3A) = \frac{47}{52}.$

The formula for the tangent of $\tan 3A$ in terms of $\tan A$ gives you the answer.

Chris

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