Inverse Circular Functions 3 Question 10
10. The numerical value of $\tan 2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}$ is … .
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Answer:
Correct Answer: 10. $-\frac{7}{17}$
Solution:
- $\tan 2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}=\tan \tan ^{-1} \frac{2 \cdot \frac{1}{5}}{1-\frac{1}{25}}-\frac{\pi}{4}$ $=\tan \tan ^{-1} \frac{5}{12}-\frac{\pi}{4}$
$$ =\frac{\tan \tan ^{-1} \frac{5}{12}-\tan \frac{\pi}{4}}{1+\tan \tan ^{-1} \frac{5}{12} \quad \tan \frac{\pi}{4}} $$
$$ =\frac{\frac{5}{12}-1}{1+\frac{5}{12} \cdot 1}=-\frac{7}{17} $$
