solve for exact solution over interval [0*,360*)

cot(x) + 2csc(x) = 3

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- Nov 8th 2006, 07:04 PMxxpl510xxI dunno what to do!!?? solve sine equation
solve for exact solution over interval [0*,360*)

cot(x) + 2csc(x) = 3 - Nov 8th 2006, 07:12 PMThePerfectHacker
Multiplby by $\displaystyle \sin x$,

$\displaystyle \cot x\sin x+2\csc x\sin x=3\sin x$

Thus,

$\displaystyle \cos x+2=3\sin x$

Square both sides,

$\displaystyle (\cos x+2)^2=9\sin^2x$

$\displaystyle \cos^2 x+4\cos x+4=9\sin^2 x$

Thus,

$\displaystyle \cos^2 x+4\cos x+4=9(1-\cos^2x)$

Thus,

$\displaystyle \cos^2 x+4\cos x+4=9-9\cos^2 x$

Thus,

$\displaystyle 10\cos^2x+4\cos x-5=0$ - Nov 8th 2006, 07:20 PMxxpl510xx
Im was close

dumb mistakes

I just didnt square the 3sin9(x) properly

thanks a bunch perfecthacker