Find $\tan (2 A)$, if $\tan (A)=-\frac{11}{60}$, and $A$ is in quadrant 4 .
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Answer

So, the final answer is $\boxed{-\frac{1320}{3479}}$.

Steps

Step 1 ：We are given that $\tan A = -\frac{11}{60}$ and we need to find $\tan (2 A)$.

Step 2 ：We know that the formula for $\tan (2 A)$ is $\frac{2 \tan A}{1 - \tan^2 A}$.

Step 3 ：Substituting $\tan A = -\frac{11}{60}$ into the formula, we get $\tan (2 A) = \frac{2 \times -\frac{11}{60}}{1 - (-\frac{11}{60})^2}$.

Step 4 ：Simplifying the above expression, we get $\tan (2 A) = -\frac{1320}{3479}$.

Step 5 ：So, the final answer is $\boxed{-\frac{1320}{3479}}$.