A) \[\frac{7}{25}\]
B) \[\frac{24}{25}\]
C) \[-\frac{24}{7}\]
D) \[\frac{8}{3}\]
Correct Answer: C
Solution :
\[\tan \left( 2{{\cos }^{-1}}\frac{3}{5} \right)=\tan \left[ {{\cos }^{-1}}\left( 2.\frac{9}{25}-1 \right) \right]\] {Since\[2{{\cos }^{-1}}x={{\cos }^{-1}}(2{{x}^{2}}-1)\]} \[=\tan {{\cos }^{-1}}\left( -\frac{7}{25} \right)=\tan {{\tan }^{-1}}\left[ \sqrt{\frac{1-\frac{49}{625}}{-\frac{7}{25}}} \right]=-\frac{24}{7}\] Therefore\[\tan \left( 2{{\cos }^{-1}}\frac{3}{5} \right)=-\frac{24}{7}\].
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