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The value of $\tan\bigg[\cos^{-1}\big(\large\frac{4}{5}\big)$$+\tan^{-1}\big(\large\frac{2}{3}\big)\bigg]$ is

$(a)\;\large\frac{6}{17}$$\qquad(b)\;\large\frac{7}{16}$$\qquad(c)\;\large\frac{16}{7}$$\qquad(d)\;None\;of\;these$

1 Answer

$\tan\big[\cos^{-1}\big(\large\frac{4}{5}\big)$$+\tan^{-1}\big(\large\frac{2}{3}\big)\big]$
$\Rightarrow \tan\bigg[\tan^{-1}\large\frac{3}{4}$$+\tan^{-1}\large\frac{2}{3}\bigg]$
$\Rightarrow \tan\bigg[\tan^{-1}\bigg(\large\frac{3/4+2/3}{1-3/4\times2/3}\bigg)\bigg]$
$\Rightarrow \large\frac{17}{12}\times \frac{12}{6}$
$\Rightarrow \large\frac{17}{6}$
Hence (d) is the correct answer.
answered Oct 9, 2013 by sreemathi.v
 

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