The correct options are
A minimum value of a is π2
B maximum value of a is 5π2
C minimum value of b is −3π2
We know that,
a3+b3+c3−3abc=(a+b+c)(a2+b2+c2−ab−bc−ca)
If a+b+c=0, then
a3+b3+c3=3abc
Now, sin3x+cos3y+(−2)3=3sinx⋅cosy⋅(−2)
⇒sinx+cosy−2=0
⇒sinx+cosy=2
⇒sinx=1,cosy=1
⇒x=π2, y=0,2π
∴a=x+y=π2,5π2
∴b=x−y=π2,−3π2