1
сtg²a*ctg²b-(cos(a+b)*cos(a-b))/(sin²a*sin²b)=
=ctg²a*ctg²b-[(cosacosb-sinasinb)(cosacosb+sinasinb)/(sin²asin²b)]=
=ctg²a*ctg²b-(cos²acos²b-sin²asin²b)/(sin²a*sin²b)=
=ctg²a*ctg²b-cos²a*cos²b/(sin²a*sin²b)+sin²a*sin²b/(sin²a*sin²b)=
=ctg²²a*ctg²b-ctg²a*ctg²b+1=1
2
ОДЗ
x-2>0⇒x>2
x-4≠0⇒x≠0
x∈(2;4) U (4;∞)
2log(5)(x-2)=-log(5)([(x-4)²]
2log(5)(x-2)=-2log(5)(x-4)
2log(5)(x-2)+2log(5)(x-4)=0
2[log(5)(x-2)+log(5)(x-4)]=0
log(5)[(x-2)(x-4)]=0
(x-2)(x-4)=1
x²-4x-2x+8=1
x²-6x+7=0
D=36-28=8
x1=(6-2√7)/2=3-√7∉ОДЗ
x2=3+√7