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Question Number 68390 by TawaTawa last updated on 10/Sep/19

Answered by som(math1967) last updated on 10/Sep/19

$$tan\left({2\tan }^{-1}\sqrt{\frac{2{cos}^2\frac{\theta }{2}}{2{sin}^2\frac{\theta }{2}}}\right)+tan\theta$$$$=tan\left\{{2\tan }^{-1}\left(\cot \frac{\theta }{2}\right)\right\}+\tan \theta$$$$=tan\left\{{2\tan }^{-1}tan(\frac{\pi }{2}-\frac{\theta }{2})\right\}+\tan \theta$$$$=tan(\pi -\theta )+tan\theta$$$$=-tan\theta +tan\theta =0$$

Commented by TawaTawa last updated on 10/Sep/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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