Inverse Trigonometric Functions Question 19
Question: $ \tan ( 2{{\cos }^{-1}}\frac{3}{5} )= $
Options:
A) $ \frac{7}{25} $
B) $ \frac{24}{25} $
C) $ -\frac{24}{7} $
D) $ \frac{8}{3} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \tan ( 2{{\cos }^{-1}}\frac{3}{5} )=\tan [ {{\cos }^{-1}}( 2.\frac{9}{25}-1 ) ] $
{Since $ 2{{\cos }^{-1}}x={{\cos }^{-1}}(2x^{2}-1) $ }
$ =\tan {{\cos }^{-1}}( -\frac{7}{25} )=\tan {{\tan }^{-1}}[ \sqrt{\frac{1-\frac{49}{625}}{-\frac{7}{25}}} ]=-\frac{24}{7} $
Therefore $ \tan ( 2{{\cos }^{-1}}\frac{3}{5} )=-\frac{24}{7} $ .
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