Evaluate `p=sum_(p=1)^(32)(3p+2)(sum_(q=1)^(10)(sin""(2qpi)/(11)-icos""(2qpi)/(11)))^(p)`, where `i=sqrt(-1)`

Evaluate sum_(k=1)^11(2+ 3^k) .

Find the value of sum_(k=1)^10[sin((2pik)/(11))-icos((2pik)/(11))],wherei=sqrt(-1).

Find the value of sum_(k=1)^10[sin((2pik)/(11))-icos((2pik)/(11))],wherei=sqrt(-1).

sum_(p=1)^(n) sum_(m=p)^(n) (("n"),("m"))(("m"),("p")) is equal to

Let S= sum_(r=1)^(5) cos (2r-1) (pi)/(11) and P=Pi_(r=1)^(4) cos (2^(r). (pi)/(15)) , then

Evaluate ( 4p - q) ^(2) - ( 4p + q) ^(2) if p =- 1 and q =2

The expression log_2 5-sum_(k=1)^4 log_2(sin((kpi)/5)) reduces to p/q, where p and q are co-prime, the value of p^2+q^2 is

A=[{:(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3)):}] and B=[{:(p_(1),q_(1),r_(1)),(p_(2),q_(2),r_(2)),(p_(3),q_(3),r_(3)):}] Where p_(i), q_(i),r_(i) are the co-factors of the elements l_(i), m_(i), n_(i) for i=1,2,3 . If (l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)) and (l_(3),m_(3),n_(3)) are the direction cosines of three mutually perpendicular lines then (p_(1),q_(1), r_(1)),(p_(2),q_(2),r_(2)) and (p_(3),q_(),r_(3)) are

If p(x)=x^2-4x+3 evaluate p(2)-p(-1)+p(1/2)