SATHEE: Inverse Circular Functions 3 Question 10

Inverse Circular Functions 3 Question 10

10. The numerical value of $\tan 2 \tan^{- 1} \frac{1}{5} - \frac{π}{4}$ is … .

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Answer:

Correct Answer: 10. $- \frac{7}{17}$

Solution:

$\tan 2 \tan^{- 1} \frac{1}{5} - \frac{π}{4} = \tan \tan^{- 1} \frac{2 \cdot \frac{1}{5}}{1 - \frac{1}{25}} - \frac{π}{4}$ $= \tan \tan^{- 1} \frac{5}{12} - \frac{π}{4}$

$= \frac{\tan \tan^{- 1} \frac{5}{12} - \tan \frac{π}{4}}{1 + \tan \tan^{- 1} \frac{5}{12} \tan \frac{π}{4}}$

$= \frac{\frac{5}{12} - 1}{1 + \frac{5}{12} \cdot 1} = - \frac{7}{17}$

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