Assertion A: `sum_(r=1)^(n-1)cos^2((rpi)/n)=n/2-1`Reason R: `cosalpha + cos(alpha + beta ) + cos(alpha +2beta) +................+ cos(alpha + (n-1)beta) =sin(nbeta/2)/sin(beta/2)cos((2alpha+(n-1)beta)/2)`

Assertion (A) sum _(r=1)^(n-1) cos^2((rpi)/(n))=(n)/(2)-1 Reasion (R) : cos alpha+ cos (alpha+ beta)+cos(alpha+2 beta)+....+cos (alpha(n-1) beta)=(sin(n beta//2))/(sin(beta//2)). Cos ((2 alpha+(n-1) beta)/(2))

Prove that: cos ^ (2) alpha + cos ^ (2) (alpha + beta) -2cos alpha cos beta cos (alpha + beta) = sin ^ (2) beta

2 sin ^(2) beta + 4 cos (alpha + beta) sin alpha sin beta + cos 2 (alpha + beta )=

Prove that for all ninN Cosalpha+cos(alpha+beta)+cos(alpha+2beta)+ . . . +cos[alpha+(n-1)beta] = (cos[alpha+((n-1)/(2))beta]"sin"((nbeta)/(2)))/("sin"(beta)/(2))

Prove that for all ninN Cosalpha+cos(alpha+beta)+cos(alpha+2beta)+ . . . +cos[alpha+(n-1)beta] = (cos[alpha+((n-1)/(2))beta]"sin"((nbeta)/(2)))/("sin"(beta)/(2))

(cos alpha + cos beta) ^ (2) + (sin alpha-sin beta) ^ (2) = 4 (cos ^ (2) (alpha + beta)) / (2)