Question

How to prove this identity.:

$17.\frac{\left(1+{\tan }^2\mathrm{\theta }\right){\sin }^2\mathrm{\theta }}{\tan \mathrm{\theta }}=\tan \mathrm{\theta }$

Answer 1

Dear student,

$$\begin{gathered} TakingL.H.S \\ \frac{\left(1+{\tan }^2\theta \right){\sin }^2\theta }{\tan \theta } \\ =\frac{se{c}^2\theta \times {\sin }^2\theta }{\tan \theta } \\ =\frac{{\displaystyle \frac{{\sin }^2\theta }{{\cos }^2\theta }}}{\tan \theta } \\ =\frac{{\tan }^2\theta }{\tan \theta } \\ =\tan \theta \\ =R.H.S \\ Henceproved. \end{gathered}$$

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