express (tan@ + (tan@)^-1)^-1 in the form asin(n@) for constants a and n

btw Ive used @ as theta

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- Sep 30th 2009, 01:45 PMSteven.MilesHelp with equation
express (tan@ + (tan@)^-1)^-1 in the form asin(n@) for constants a and n

btw Ive used @ as theta - Sep 30th 2009, 02:27 PMskeeter
$\displaystyle (\tan{t} + \cot{t})^{-1}$

$\displaystyle \frac{1}{\tan{t} + \cot{t}}$

multiply by $\displaystyle \frac{\sin{t}\cos{t}}{\sin{t}\cos{t}}$ ...

$\displaystyle \frac{\sin{t}\cos{t}}{\sin^2{t} + \cos^2{t}}$

$\displaystyle \sin{t}\cos{t}$

$\displaystyle \frac{1}{2}\sin(2t)$