Question Number 212615 by MrGaster last updated on 19/Oct/24
![Verify the equation:tan nx=Σ_(k=1) ^([((n+1)/2)]) (−1)^(k−1) ((n),((2k−1)) ) tan^(2k−1) x/Σ_(k=0) ^([(n/2)]) (−1)^k ((n),((2k)) )tan^(2k) x](https://www.tinkutara.com/question/Q212615.png)
$$\mathrm{Verify}\:\mathrm{the}\:\mathrm{equation}:\mathrm{tan}\:{nx}=\underset{{k}=\mathrm{1}} {\overset{\left[\frac{{n}+\mathrm{1}}{\mathrm{2}}\right]} {\sum}}\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} \begin{pmatrix}{{n}}\\{\mathrm{2}{k}−\mathrm{1}}\end{pmatrix}\:\mathrm{tan}^{\mathrm{2}{k}−\mathrm{1}} {x}/\underset{{k}=\mathrm{0}} {\overset{\left[\frac{{n}}{\mathrm{2}}\right]} {\sum}}\left(−\mathrm{1}\right)^{{k}} \begin{pmatrix}{{n}}\\{\mathrm{2}{k}}\end{pmatrix}\mathrm{tan}^{\mathrm{2}{k}} {x} \\ $$