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Question Number 204293 by depressiveshrek last updated on 11/Feb/24

$$\mathrm{Prove}\mathrm{the}\mathrm{following}\mathrm{trig}\mathrm{identity}:$$$$\frac{2\sin \alpha +\sin 3\alpha +\sin 5\alpha }{\cos \alpha -2\cos 2\alpha +\cos 3\alpha }=\frac{2\cos 2\alpha }{\tan \frac{\alpha }{2}}$$

Commented by Frix last updated on 11/Feb/24

$$\mathrm{Try}.$$$$\alpha =\frac{\pi }{6}\Rightarrow \mathrm{lhs}=-5(2+\sqrt{3})\mathrm{rhs}=2+\sqrt{3}$$$$\alpha =\frac{\pi }{2}\Rightarrow \mathrm{lhs}=1\mathrm{rhs}=-2$$$$...$$

Answered by Frix last updated on 11/Feb/24

$${\mathrm{It}}^{\prime }\mathrm{s}\mathrm{false}.$$

Commented by depressiveshrek last updated on 11/Feb/24

$$\mathrm{Why}?$$

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