Question

3tgx - 2ctgx=1
x =?

va rog !!

Answer 1

tinem, cont ca ctgx=1/tgx
ecuatia devine

3tgx-2/tgx=1
folosim substitutia
tgx=t
atunci
 3t-2/t=1
3t²-2-t=0
3t²-t-2=0
t1,2=(1+-√(1+24))/6=(1+-5)/6
t1=-4/6=-2/3
t2=(6/6)=1

tgx=-2/3  x= arctg(-2/3)+kπ=-arctg(2/3)+kπ=kπ-arctg(2/3)
tgx=1    x=arctg1+kπ=π/4+kπ   k∈Z
x∈(kπ-arctg(2/3)) ∪ (π/4+kπ)