1) cos(5β) +sin(2β)sin3β)=cos(5β) +(cos(2β-3β) -cos(2β+3β) ) /2=
=cos(5β) +(cos(-β) -cos(5β) )/2=cos(5β) /2 +cosβ;
3) x>0; y>0
log(3) y -log(3)x=1; log(3) (y/x)=1; y/x=3; y=3x;
x^log(3) (3x) + 2(3x)^log(3) x=3^3;
x^(log(3) 3 +log(3) x) + 2*3^log(3) x *x^log(3) x =3^3
x*x^log(3) x +2*x *x^log(3) x=3^3
3x *x^log(3) x=3^3
log(3) 3+log(3) x +log(3) (x^log(3) x)=log(3) (3^3)
1+log(3) x +log(3) x *log(3) x)=3
t=log(3) x; t^2+t-2=0; D=1^2 +8=9=3^2; t1=(-1-3)/2=-2; t2=1
log(3) x=-2 ili log(3) x=1
x=3^(-2) x=3^1
x=1/9 x=3
y=3*(1/9)=1/3 y=3*3=9
ответ(1/9; 1/3); (3;9)