1)sinx+siny=2sin((x+y)/2)·cos((x-y)/2)
sinx+sin5x=2cos2x
2sin3x·cos2x=2cos2x
cos2x=0
2x=(π/2)+πk
x=(π/4)+(π/2)k
2sin3x=2
sin3x=1
3x=(π/2)+2πk
x=(π/6)+((2π)/3)k
k∈Z
Ответ;
x=(π/4)+(π/2)k
x=(π/6)+((2π)/3)k
k∈Z
2)3lg(x²)-lg²x=9
6lgx-lg²x=9
пусть lgx=t, тогда
6t-t²=9
t²-6t+9=0
D=0
t=3
lgx=3
x=1000