Question : If $\cot A = \frac{15}{8}$, then what will be the value of $\tan 2 A ?$
Option 1: $\frac{200}{161}$
Option 2: $\frac{240}{161}$
Option 3: $\frac{240}{173}$
Option 4: $\frac{220}{171}$
Correct Answer: $\frac{240}{161}$
Solution :
$\cot A = \frac{15}{8}$
So, $\tan A = \frac{8}{15}$
Now, $\tan 2A = \frac{2 \ tan A}{1-\tan^2A}$
= $\frac{2 \times \frac{8}{15}}{1-(\frac{8}{15})^2}$
= $\frac{\frac{16}{15}}{\frac{161}{225}}$
= $\frac{16 \times 225}{15 \times 161}$
= $\frac{240}{161}$
Hence, the correct answer is $\frac{240}{161}$.
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