If 4 = 3 , find tan^2 + ^2 - Vidyadip

Question

If $4 \sin\theta = 3 \cos\theta $, find $tan^2\theta + \cot^2\theta$

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Answer

$4 \sin \theta=3 \cos \theta $
$ \Rightarrow \frac{\sin \theta}{\cos \theta}=\frac{3}{4}$
$ \Rightarrow \tan \theta=\frac{\sin \theta}{\cos \theta}=\frac{3}{4} $
$\Rightarrow \cot \theta=\frac{1}{\tan \theta}=\frac{4}{3}$
$ \tan ^2 \theta+\cot ^2 \theta $
$ =\left(\frac{3}{4}\right)^2+\left(\frac{4}{3}\right)^2$
$ =\frac{9}{16}+\frac{16}{9} $
$ =\frac{81+256}{144} $
$ =\frac{337}{144} .$

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