If `A=[[sin((3+r)(pi)/(4)),1,0],[cos((3+r)(pi)/(4)),1,1],[(1)/(7),1,1]],` then value of `sum_(r=0)^(6)|A|` is equal to

sin^(-1)(cos((3 pi)/(4)))

If A-[[sin((3 pi)/(2)),sin pi,2],[cos((2 pi)/(3)),1,k],[cos pi,-4,tan((pi)/(4))]] is a singular matrix, then the value of k is

The value of sum_(r=0)^(10)cos^(3)((r pi)/(3)) is

Calculate 4 sin (1+(pi)/(6)) cos (1+(pi)/(3))

If a=cos(4 pi)/(3)+i sin(4 pi)/(3) then the value of (1+a)^(3n) is

sin^(2)(pi)/(6)+cos^(2)(pi)/(3)-tan^(2)-(1)/(2)(pi)/(4)=-(1)/(2)

If a=cos((4 pi)/(3))+i sin((4 pi)/(3)), then the value ((1+a)/(2))^(3n)

If a=cos((4 pi)/(3))+i sin((4 pi)/(3)), then the value ((1+a)/(2))^(3n)

Let Q = [{: (cos ""(pi)/(4) , - sin""(pi)/(4)),(sin""(pi)/(4), cos""(pi)/(4)):}] and x = [{:((2)/(sqrt(2))),((1)/(sqrt(2))):}] then Q^(3) x is equal to