1) sinx - cosx =0
sinx - cosx = 0
cosx cosx cosx
tgx - 1 =0
tgx = 1
x= π/4 + πk, k∈Z
3) tg3x = √3/3
3x= π/6 + πk, k∈Z
x=π/18 + (π/3)k, k∈Z
2) 5 ctg²x - 8ctgx +3=0
y=ctgx
5y² -8y +3=0
D=64-60=4
y₁ = 8-2 = 0.6
10
y₂ = 8+2 = 1
10
При у=0,6
ctgx=0.6
x= arcctg 0.6 +πk, k∈Z
При у=1
ctgx=1
x=π/4 + πk, k∈Z
4) tg(x/2) * (1+cosx)=0
1) tg(x/2)=0
x/2=πk, k∈Z
x=2πk, k∈Z
2) 1+cosx=0
cosx= -1
x=π + 2πk, k∈Z
5) cos² x + sinx cosx -1=0
cos² x + sinx cosx - (cos² x+sin² x) =0
cos² x +sinx cosx -cos²x - sin² x =0
sinx cosx - sin² x =0
sinx (cosx - sinx) =0
1) sin x =0
x=πk, k∈Z
2) cosx - sinx =0
cosx - sinx = 0
cosx cosx cosx
1-tgx =0
tgx=1
x=π/4 + πk, k∈Z