Originally Posted by

**scherz0** Dear all,

For the following equation which I have to solve for $\displaystyle t$, I am getting an expression that differs from the given answer and I do not understand why.

I have made two attempts, both posted below. Thank you very much for your help.

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**Show: **$\displaystyle \tan(t\sqrt{5}) = \frac{-2 \times \sqrt{5}}{\alpha + 2} \Rightarrow t = \frac{1}{\sqrt{5}}\left(\pi - arctan\frac{2\sqrt{5}}{\alpha + 2}\right)$, where $\displaystyle \alpha \geq 0 $

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__Solution 1: __$\displaystyle \tan(t\sqrt{5}) = \frac{-2 \times \sqrt{5}}{\alpha + 2} $

$\displaystyle \Rightarrow t\sqrt{5} = \arctan\frac{-2\sqrt{5}}{\alpha + 2} $

$\displaystyle \Rightarrow t = -\frac{1}{\sqrt{5}}\arctan\frac{2\sqrt{5}}{\alpha + 2} $,

where I have used the facts that $\displaystyle \arctan(-x) = -x$ and took the arctangent of the original equation.