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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Trignometry

The value of $\cos[2\tan^{-1}(-7)]$ is

$(a)\;\large\frac{49}{50}$$\qquad(b)\;\large\frac{-49}{50}$$\qquad(c)\;\large\frac{24}{25}$$\qquad(d)\;-\large\frac{24}{25}$

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1 Answer

$\cos(2\tan^{-1}(-7))=\cos\big[\cos^{-1}\big(\large\frac{1-49}{1+49}\big)\big]$
$\qquad\qquad\qquad\;\;=\cos\big[\cos^{-1}\big(\large\frac{-48}{50}\big)\big]$
$\qquad\qquad\qquad\;\;=\cos\big[\pi-\cos^{-1}\big(\large\frac{48}{50}\big)\big]$
$\qquad\qquad\qquad\;\;=\cos\big[-\cos^{-1}\big(\large\frac{48}{50}\big)\big]$
$\qquad\qquad\qquad\;\;=-\cos\cos^{-1}\big(\large\frac{48}{50}\big)$
$\qquad\qquad\qquad\;\;=\large\frac{-48}{50}$
$\qquad\qquad\qquad\;\;=\large\frac{-24}{25}$
Hence (d) is the correct answer.
answered Oct 11, 2013 by sreemathi.v
 

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