cosx+cosy+cosz=4sinx/2*siny/2*sinz/2+1

u ovom zadatku koristi se da je x+y+z=180

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Re: trigonometrija
vriskica18/9/2008, 16:55

ma to sam i mislio...
tezak je, al uspio sam!
cosx+cosy+cosz=(cosx+cosy)+cosz=
btw. cosz=cos(180°-x-y)=-cos(x+y) so
=2cos[(x+y)/2]cos[(x-y)/2]-cos(x+y)
=2cos[(x+y)/2]cos[(x-y)/2]-{2cos&#178[(x+y)/2]-1}
=2cos[(x+y)/2]{cos[(x-y)/2]-cos[(x+y)/2]}+1
=2cos[(x+y)/2]{2sin[(x-y+x+y)/4]sin[(x-y-x-y)/4]}+1
=4cos[(180°-z)/2]sin(x/2)sin(-y/2)+1
=4cos(90°-z/2)sin(x/2)sin(-y/2)+1
=4sin(-z/2)sin(x/2)sin(-y/2)+1
=4sin(z/2)sin(x/2)sin(y/2)+1

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Re: trigonometrija
Gino18/9/2008, 17:50

e hvala ti

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Re: trigonometrija
vriskica18/9/2008, 18:47

nadam se da je sve jasno... dosta je nepregledno, al... ako ne nis prepises na papir pa bude jasnije po tom pitanju

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Re: trigonometrija
Gino18/9/2008, 19:05

Re: trigonometrija
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