Inverse Trigonometric Functions Question 20
Question: $ \tan [ 2{{\tan }^{-1}}( \frac{1}{5} )-\frac{\pi }{4} ]= $
[IIT 1984]
Options:
A) $ \frac{17}{7} $
B) $ -\frac{17}{7} $
C) $ \frac{7}{17} $
D) $ -\frac{7}{17} $
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Answer:
Correct Answer: D
Solution:
$ \tan [ 2{{\tan }^{-1}}( \frac{1}{5} )-\frac{\pi }{4} ]=\tan [ {{\tan }^{-1}}\frac{\frac{2}{5}}{1-\frac{1}{25}}-{{\tan }^{-1}}(1) ] $
$ =\tan [ {{\tan }^{-1}}\frac{5}{12}-{{\tan }^{-1}}(1) ]=\tan {{\tan }^{-1}}( \frac{\frac{5}{12}-1}{1+\frac{5}{12}} )=-\frac{7}{17} $ .
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