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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Trignometry
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If $\alpha+\beta=\large\frac{\pi}{2}$ and $\beta+\gamma=\alpha$ then $\tan\alpha$ equals

$\begin{array}{1 1}(a)\;2(\tan\beta+\tan\gamma)&(b)\;\tan\beta+\tan\gamma\\(c)\;\tan\beta+2\tan\gamma&(d)\;2\tan\beta+\tan\gamma\end{array}$

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1 Answer

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Given :
$\alpha =\large\frac{\pi}{2}$$-\beta$
$\tan\alpha=\cot \beta=\large\frac{1}{\tan\beta}$
$\beta+\gamma=\alpha$
$\Rightarrow \large\frac{\tan\beta+\tan\gamma}{1-\tan\beta\tan\gamma}$
$\Rightarrow \tan\alpha$
$\Rightarrow \large\frac{1}{\tan\beta}$
$\tan^2\beta+2\tan\beta\tan\gamma=1$
$\tan\beta(\tan\beta+2\tan\gamma)=1$
$\tan\beta+2\tan\gamma=\large\frac{1}{\tan\beta}$
$\Rightarrow \tan\alpha$
Hence (c) is the correct option.
answered Oct 10, 2013 by sreemathi.v
 

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