$t$ for tan
If we write $t = \tan \theta$, then the following equations are true.
\begin{align*}
\tan(2\theta) &= \frac{2t}{1-t^2}, \\
\sin(2\theta) &= \frac{2t}{1+t^2}, \\
\cos(2\theta) &= \frac{1-t^2}{1+t^2}.
\end{align*}
Can you use this diagram to obtain these formulae?
For what range of values of $\theta$ does this argument work?
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