Question

решить неравенство 2tg x+1≤0

Answer 1

2tgx+1≤0
2tgx≤-1
tgx≤-0,5
x∈(-π/2+πk;-arctg0,5+πk,k∈z]

Answer 2

2tg(x)-ctg(x)+1=0

2tg(x)-1/tg(x) +1=0

tg(x)=t

2t-1/t +1=0

2t^2-1+t=0

2t^2+t-1=0

D=b^2-4ac=9

t1,2=(-b±√D)/2a

t1=(-b+√D)/2a=(-1+3)/4=0,5

t2=(-b+√D)/2a=(-1-3)/4=-1

a) tg(x)=0,5=> x=arctg(0,5)+pi*n

б) tg(x)=-1 => x=arctg(-1)+pi*n=> x=3pi/4  +pi*n