sum_(x=1)^(10)cos^(3)x(pi)/(3)=?

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

sum _(r=1) ^(10) cos ^(3) "" (r pi)/(3) =

If A=sum_(r=1)^(3)"cos"(2r pi)/(7) and B=sum_(r=1)^(3)"cos"(2^(r )pi)/(7) then :

If A= sum _(r=1)^(3)"cos"(2r pi)/(7) and B=sum_(r=1)^(3)"cos"(2^(r )pi)/(7) , then :

If A= sum _(r=1)^(3)"cos"(2r pi)/(7) and B=sum_(r=1)^(3)"cos"(2^(r )pi)/(7) , then :

Matching the items of Column-I with the items Column-II {:("Column-I", "Column-II"), ("A) If "cos^(-1)lambda+cos^(-1)mu+cos^(-1)gamma=3pi" then "lambdamu+mugamma+gammalambda" is","p) "2n), ("B) If "sum_(i=1)^(10)cos^(-1)x=0" then "sum_(i=1)^(10)x_(i)" is", "q) "(sin^(-1)x-pi/6)), ("C) If "sum_(i=1)^(2n)sin^(-1)x_(i)=npi" then "sum_(i=1)^(2n)x_(i)" is", "r) "10),("D) The value of "sin^(-1){sqrt(3)/2x-1/2sqrt(1-x^(2))}"," (-1/2 le x le 1/2)" is", "s) "3):}

If x in(0,pi/2) and cos x=1/3, then prove that sum_(n=0)^(oo)(cos nx)/(3^(n))=(3(3-cos x))/(10-6cos x+cos^(2)x)

Prove that cos^(2)x+cos^(2)(x+(pi)/(3))+cos^(2)(x-(pi)/(3))=(3)/(2)

Prove that cos^(2)x+cos^(2)(x+(pi)/(3))+cos^(2)(x-(pi)/(3))=(3)/(2)