Bellino
Moderatore: tutor
Visto che stasera ho mangiato fuori nn ho di questi problemi, però mi devo sbrigare perchè se nn pulisco i pavimenti stanotte nn posso dormire in casa...
<BR>
<BR>Dunque:
<BR>
<BR>tg(x+y+z)=[-tg(x)*tg(y)*tg(z) + tg(x)+tg(y)+tg(z)]/ /[-tg(x)*tg(y)-tg(x)*tg(z)-tg(y)*tg(z)+1]
<BR>
<BR>(t-a)*(t-b)*(t-c)=t^3 -(a+b+c)*t^2 + (ab+bc+ca)*t - abc
<BR>X^3 + pX^2 + qX + r=0 p=-(a+b+c) q=ab+bc+ca r=abc
<BR>p=0
<BR>q=-10
<BR>r=11
<BR>
<BR>ora, x=arctg(a) y=arctg(b) z=arctg(c)
<BR>
<BR>x+y+z=arctg ( tg(x+y+z) )
<BR>
<BR>tg(x)=a tg(y)=b tg(z)=c
<BR>
<BR>x+y+z=arctg([-tg(x)*tg(y)*tg(z) + tg(x)+tg(y)+tg(z)]/ /[-tg(x)*tg(y)-tg(x)*tg(z)-tg(y)*tg(z)+1])=arctg([-abc + a + b+c]/[-ab-bc-ca+1])=arctg([r-p]/[1-q])=arctg([11-0]/[1+10])=arctg(1)=Pi/4
<BR>
<BR>Dunque:
<BR>
<BR>tg(x+y+z)=[-tg(x)*tg(y)*tg(z) + tg(x)+tg(y)+tg(z)]/ /[-tg(x)*tg(y)-tg(x)*tg(z)-tg(y)*tg(z)+1]
<BR>
<BR>(t-a)*(t-b)*(t-c)=t^3 -(a+b+c)*t^2 + (ab+bc+ca)*t - abc
<BR>X^3 + pX^2 + qX + r=0 p=-(a+b+c) q=ab+bc+ca r=abc
<BR>p=0
<BR>q=-10
<BR>r=11
<BR>
<BR>ora, x=arctg(a) y=arctg(b) z=arctg(c)
<BR>
<BR>x+y+z=arctg ( tg(x+y+z) )
<BR>
<BR>tg(x)=a tg(y)=b tg(z)=c
<BR>
<BR>x+y+z=arctg([-tg(x)*tg(y)*tg(z) + tg(x)+tg(y)+tg(z)]/ /[-tg(x)*tg(y)-tg(x)*tg(z)-tg(y)*tg(z)+1])=arctg([-abc + a + b+c]/[-ab-bc-ca+1])=arctg([r-p]/[1-q])=arctg([11-0]/[1+10])=arctg(1)=Pi/4
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- Messaggi: 576
- Iscritto il: 01 gen 1970, 01:00
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