A) \[\frac{49}{50}\]
B) \[-\frac{49}{50}\]
C) \[\frac{24}{25}\]
D) \[-\frac{24}{25}\]
E) \[\frac{48}{49}\]
Correct Answer: D
Solution :
\[\cos [2{{\tan }^{-1}}(-7)]=\cos \left[ {{\cos }^{-1}}\left( \frac{1-(49)}{1+49} \right) \right]\] \[=\cos \left[ {{\cos }^{-1}}\left( -\frac{48}{50} \right) \right]\] \[=\cos \left[ \pi -{{\cos }^{-1}}\left( \frac{48}{50} \right) \right]\] \[=-\cos {{\cos }^{-1}}\left( \frac{48}{50} \right)\] \[=-\frac{48}{50}=-\frac{24}{25}\]
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