7√3sinx-cos2x-10=1
7√3sinx-1+2sin²x-10-1=0
sinx=a
2a²+7√3a-12=0
D=147+96=243
a1=(-7√3-9√3)/4=-4√3⇒sinx=-4√3<-1 нет решения<br>a2=(-7√3+9√3)/4=√3/2⇒sinx=√3/2
x=π/3+2πk U x=2π/3+2πk
3π/2≤π/3+2πk≤3π U 3π/2≤2π/3+2πk≤3π
9≤2+12k≤18 U 9≤4+12k≤18
7≤12k≤16 U 5≤12k≤14
7/12≤k≤16/12 U 5/12≤k≤14/12
k=1⇒x=π/3+2π=7π/3 U x=2π/3+2π=8π/3
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проверка
x=7π/3
log(8)(7√3*sin7π/3-cos14π/3-10)=log(8)(7√3*√3/2-(-1/2)-10)=
=log(8)(10,5+0,5-10)=log(8)1=0
0=0
x=8π/3
log(8)(7√3sin8π/3-cos16π/3-10)=log(8)(7√3*√3/2-(-1/2)-10)=
=log(8)(10,5+0,5-10)=log(8)1=0
0=0