sum_(x=1)^(6)(605(2x pi)/(7)-(i sin2x pi)/(7))=?

sum_(m=1)^(32)m[sum_(k=1)^(6)sin2k(pi)/(7)-i cos2k(pi)/(7)]

sum_ (k = 1) ^ (6) (sin, (2 pi k) / (7) -i cos, (2 pi k) / (7)) =?

The number of real solution of the equation sin^(-1) (sum_(i=1)^(oo) x^(i +1) -x sum_(i=1)^(oo) ((x)/(2))^(i)) = (pi)/(2) - cos^(-1) (sum_(i=1)^(oo) (-(x)/(2))^(i) - sum_(i=1)^(oo) (-x)^(i)) lying in the interval (-(1)/(2), (1)/(2)) is ______. (Here, the inverse trigonometric function sin^(-1) x and cos^(-1) x assume values in [-(pi)/(2), (pi)/(2)] and [0, pi] respectively)

The number of real solution of the equation sin^(-1) (sum_(i=1)^(oo) x^(i +1) -x sum_(i=1)^(oo) ((x)/(2))^(i)) = (pi)/(2) - cos^(-1) (sum_(i=1)^(oo) (-(x)/(2))^(i) - sum_(i=1)^(oo) (-x)^(i)) lying in the interval (-(1)/(2), (1)/(2)) is ______. (Here, the inverse trigonometric function sin^(-1) x and cos^(-1) x assume values in [-(pi)/(2), (pi)/(2)] and [0, pi] respectively)

let a=sum_(r=1)^(6)cos((r pi)/(7)),b=sum_(r=1)^(6)cos^(2)((r pi)/(7)),c=sum_(1<=i)sum_(j<=6)cos((i pi)/(7))cos((j pi)/(7)) then find the value of (a-b)/(c)

prod_ (k = 1) ^ (6) (sin ((2k pi) / (7)) - i cos ((2k pi) / (7))) =

(sin((2 pi)/(7))+sin((4 pi)/(7)) -sin((6 pi)/(7)))/(sin((pi)/(7))sin((3 pi)/(7))sin((5 pi)/(7))) is equal to

If f(x)=x^(11)+sin^(3)(35x)+111x, then the value of f^(-1)(sin((pi)/(5)))+f^(-1)(sin(6(pi)/(5)))+f^(-1)(((sin pi)/(7)))+f^(-1)(sin(8(pi)/(7)))