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Mathematics
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Trig
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Grit.
lol
|dw:1315660157994:dw| Determine the exact value of \[\tan \alpha\]
The disfigured "a" is alpha
\[\tan( \alpha+60) = \frac{40}{8} =5\]\[\tan(\alpha+60)=5\]\[\alpha +60 = \tan^{-1}(5)\]\[\alpha=\tan^{-1}(5) -60\] find the value of alpha, then find \[\tan \alpha\]
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\[ \tan(\alpha + 60^o ) = 40/8 = 5\] \[ \alpha + 60^o = \tan^{-1}{(5)}\] \[ \alpha = \tan^{-1}{(5)} - 60^o\] \[ \tan(\alpha) = \tan(\tan^{-1}{(5)} - 60^o)\]
The exact answer is ((5-√3))/((1+5√(3) ))
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