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Home Q & A Board Science-Related Homework Help Mathematics
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Firas Firas
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11 years ago
I was able to do it, but it took up a whole sheet of paper, front and back.  Is there a quick(er) way to this?  Very interested to know...please post how you did it.  10 POINTS WILL BE AWARDED.

Find the exact solutions of the equation in the interval [0, 2?).

tan 2x - 2 cos x = 0

Looks harmless, I know, but it's pure evil I tell you.
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nwobienwobie
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11 years ago
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11 years ago
tan 2x = 2 cos x

2 cos x = 2 sin 2x/cos 2x = 2 sin x cos x /(1 - 2 sin^2 x)

1 - 2 sin ^2 x = sin x, plus you have to check the cases sin^2 x = 1/2 or cos  = 0.

The main case is a simple quadratic equation in sin x that can be solved by the FOIL method.
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