x+y+z= π ..

AnaMaria2323 · Mesaj de **AnaMaria2323** » 15 Mai 2018, 19:45

x+y+z = π
Arătați ca c $ctg\frac{x}{2}+ctg\frac{y}{2}+ctg\frac{z}{2} = ctg\frac{x}{2}*ctg\frac{y}{2}*ctg\frac{z}{2}$

Felixx · Mesaj de **Felixx** » 15 Mai 2018, 23:01

$ctg\frac{A}{2}=ctg\left ( \frac{\pi }{2}-\frac{B+C}{2} \right )=tg\frac{B+C}{2}=tg\left ( \frac{B}{2}+\frac{C}{2} \right )=\frac{tg\frac{B}{2}+tg\frac{C}{2}}{1-tg\frac{B}{2}tg\frac{C}{2}}=\frac{\frac{1}{ctg\frac{B}{2}}+\frac{1}{ctg\frac{C}{2}}}{1-\frac{1}{ctg\frac{B}{2}}\frac{1}{ctg\frac{C}{2}}}=\frac{ctg\frac{C}{2}+ctg\frac{B}{2}}{ctg\frac{B}{2}ctg\frac{C}{2}-1}$
De aici rezulta usor identitatea din enunt.

Integrator · Mesaj de **Integrator** » 16 Mai 2018, 08:15

AnaMaria2323 scrie: ↑
15 Mai 2018, 19:45
x+y+z = π
Arătați ca c $ctg\frac{x}{2}+ctg\frac{y}{2}+ctg\frac{z}{2} = ctg\frac{x}{2}*ctg\frac{y}{2}*ctg\frac{z}{2}$

Bună dimineața,

Pentru ce alte valori ale sumei $x+y+z$ mai poate exista egalitatea $ctg\frac{x}{2}+ctg\frac{y}{2}+ctg\frac{z}{2} = ctg\frac{x}{2}\cdot ctg\frac{y}{2}\cdot ctg\frac{z}{2}$

Toate cele bune,

Integrator

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x+y+z= π ..

x+y+z= π ..

Re: x+y+z= π ..

Re: x+y+z= π ..