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Use the tangent addition formula.

May 14, 2026Mathematics

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here's the solution for Item 9:

a) Prove that $\tan 2A = \frac{2\tan A}{1-\tan^2 A}$ .

Use the tangent addition formula.
The tangent addition formula states that $\tan(X+Y) = \frac{\tan X + \tan Y}{1 - \tan X \tan Y}$ .
Substitute $X=A$ and $Y=A$ into the formula.
$\tan(A+A) = \frac{\tan A + \tan A}{1 - \tan A \tan A}$ $\tan 2A = \frac{2\tan A}{1 - \tan^2 A}$
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