sinx-cosx=1
sinx=1+cosx
2sin(x/2)cosx/2=2cos²(x/2)
sin(x/2) cos(x/2)=cos²(x/2)
cos(x/2)(sin(x/2)-cos(x/2))=0
cos(x/2)=0
x/2=π/2...x=π∉[0;π/2)
sin(x/2)-cos(x/2)=0
sin(x/2)=cos(x/2)
tg(x/2)=1
x/2=π/4
x=π/2∉[0;π/2)
ecuatia nu are solutii in[0;π/2)
ALTFEL
sinx<cos x, pt x∈[0;π/4) dci sinx-cosx<0<1,eciuatia nu atresoluitiiin [0;π/4)
sinx=cosx, pt x=π/4 , sinx-cosx=0<1, π/4 nu este solutie
pt x∈(π/4;π/2) sinx creste cos x , scade
sinx-cosx crescator
sup (sinx-cosx)=1
dar x->π/2 , x≠π/2
cand x->π/2 , (sinx-cosx)->1 dar x<π/2⇒sinx-cosx<1
sau, cum π/2∉[0,π/2) , functia sinx-cosx nefiind definita in π/2 ,nu isi atinge marginea superioara (nu are un maxim)
cum nu exista x∈[0;π/2) ptcare sinx-cosx=1, nu are sens sa calculam ctgx
Obs
probabil TEXT GRESIT
posibisa fi fost cosx-sinx=1, caz in care x=0∈[0;π/2)
sau sinx-cosx=-1, idem, x=0 ∈[0;π/2)
sau sinx-cosx=0, caz incare x=π/4∈[0;π/2)
