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Question Number 209768 by OmoloyeMichael last updated on 20/Jul/24

$$\mathit{E}\mathit{x}\mathit{p}\mathit{r}\mathit{e}\mathit{s}\mathit{s}\mathit{t}\mathit{a}\mathit{n}\left(3\right)\mathit{i}\mathit{n}\mathit{s}\mathit{u}\mathit{r}\mathit{d}\mathit{f}\mathit{o}\mathit{r}\mathit{m}$$

Answered by Frix last updated on 22/Jul/24

$$\tan (\alpha -\beta )=\frac{\tan \alpha -\tan \beta }{1+\tan \alpha \tan \beta }$$$$\mathrm{Use}\alpha =18°\mathrm{and}\beta =15°.\mathrm{The}\mathrm{only}\mathrm{problem}\mathrm{is}$$$$\mathrm{to}\mathrm{factorize}\mathrm{it}...$$$$\mathrm{I}\mathrm{get}$$$$\tan 3°=\frac{(-7+2\sqrt{15}-3\sqrt{5}+4\sqrt{3})\sqrt{5-2\sqrt{5}}+(4-\sqrt{15}+2\sqrt{5}-3\sqrt{3})}{2}$$

Commented by OmoloyeMichael last updated on 22/Jul/24

$$\mathit{t}\mathit{h}\mathit{a}\mathit{n}\mathit{k}\mathit{s}\mathit{s}\mathit{i}\mathit{r}$$

Commented by Frix last updated on 22/Jul/24

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