Inverse Circular Functions Ques 19
- The numerical value of $\tan 2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}$ is … .
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Answer:
Correct Answer: 19.$-\frac{7}{17}$
Solution:
Formula:
- $\tan [2 \tan ^{-1} (\frac{1}{5})-\frac{\pi}{4}]=\tan [\tan ^{-1} (\frac{2 \cdot \frac{1}{5}}{1-\frac{1}{25}})-\frac{\pi}{4}]$
$=\tan [\tan ^{-1} (\frac{5}{12})-\frac{\pi}{4}]$
$ =\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} $
BETA
