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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Trignometry
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The value of $\cot (cosec^{-1}\large\frac{5}{3}$$+\tan^{-1}\large\frac{2}{3})$ is

$(a)\;\large\frac{6}{17}$$\qquad(b)\;\large\frac{3}{17}$$\qquad(c)\;\large\frac{4}{17}$$\qquad(d)\;\large\frac{5}{17}$

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1 Answer

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We know $cosec^{-1}\big(\large\frac{5}{3}\big)$$=tan^{-1}\large\frac{3}{4}$
$\Rightarrow \cot(\tan^{-1}\large\frac{3}{4}$$+\tan^{-1}\large\frac{2}{3})$
$\Rightarrow \cot\tan^{-1}\bigg[\large\frac{\Large\frac{3}{4}+\frac{2}{3}}{1-\Large\frac{1}{2}}\bigg]$
$\Rightarrow \cot\{\tan^{-1}\big(\large\frac{17}{6}\big)\}$
$\Rightarrow \large\frac{1}{\tan}$$\times \tan^{-1}$$\big(\Large\frac{17}{6}\big)$
$\Rightarrow \large\frac{1}{\tan}$$\times \tan$$\big(\Large\frac{6}{17}\big)$
$\Rightarrow \large\frac{6}{17}$
Hence (a) is the correct answer.
answered Oct 11, 2013 by sreemathi.v
edited Mar 3, 2014 by meenakshi.p
 

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