1) 54^(1/3)*16^(1/2)/250^(1/3)=
(2*27)^(1/3)*4/(2*125)^(1/3)=
3*2^(1/3)*4/(5*2^(1/3))=3*4/5=12/5
2) log3(4)+2log3(1/2)-1=
2log3(2)-2log3(2)-1=-1
3) sin a*cos(-b)-sin(a-b)=
sin a*cos b-sin a*cos b+cos a*sin b=
cos a*sin b
4) 2 + (2t-1)/(t+2) = (4t+3)/(2t+1)
Область определения
t=/=-2; t=/=-1/2
2(t+2)(2t+1)+(2t-1)(2t+1)=(4t+3)(t+2)
4t^2+10t+4+4t^2-1=4t^2+11t+6
4t^2-t-3=0
(t-1)(4t+3)=0
t1=1; t2=-3/4
8) tg(3Π/2-x)=1
3Π/2-x=Π/4-Π*k
x=3Π/2-Π/4+Π*k=270-45+180*k
x=225+180*k
На промежутке [0;90] корень
x=225-180=45°