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Prove:

\begin{align} \tan(A) + \cot(A) & = 2 \text{cosec}(2A)\\ \tan(45^{\circ}+A^{\circ}) - \tan(45^{\circ}-A^{\circ}) & = 2 \tan(2A^{\circ})\\ \text{cosec}(2A) + \cot(2A) & = \cot(A) \end{align}

I have got all the formulas that I need but I just couldn't solve these. Some help, please?

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    For the second one: $\tan(u+v)=\frac{\tan\,u+\tan\,v}{1-\tan\,u\tan\,v}$ and $\tan 45^\circ=1$.2011-08-07
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    @Sophia: Do you mean $\csc(2\textrm A)$ for cosec($2\textrm A$)?2011-08-08
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    I have solved the 1st and 3rd question, but I still can't get the second question! Anymore further hints please?2011-08-08
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    I gave a formula you can use for both the left and right hand sides... $u+u=2u$, right?2011-08-09

3 Answers 3