Explicație pas cu pas:
fie:t=tg(x/2)
sinx=2t/(1+t²)
cosx=(1-t²)/(1+t²)
(-t²+2t+1)/(1+t²)=7/5
7+7t²=-5t²+10t+5
12t²-10t+2=0
6t²-5t+1=0
delta=25-24=1
t=(5+1)/12=1/2
t=(5-1)/12=1/3
x€(0,pi/4)
tg(x/2)€(0,tg(pi/8) )
tg(pi/8)=sin(pi/8)/cos(pi/8)
sin(pi/8)=sin(pi/4/2)=radical((1-rad2/2)/2)
radical((1-1,4/2)/2)=radical(0,15)=radical15/10=0,38
deci tg(x/2)€(0;0,38)
deci tg(x/2)=1/3
Raspuns:1/3
Bafta!
