`(cos(pi)/(6)+isin(pi)/(6))^(7)`

For a complex number Z. If arg(Z) in (-pi, pi] , then arg{1+cos.(6pi)/(7)+isin.(6pi)/(7)} is (here i^(2)=-1 )

Find the value of expression (cos(pi/2)+isin(pi/2))(cos(pi/(2^2))+isin(pi/(2^2))).......oo

If w=cos""(pi)/(n)+isin""(pi)/(n) then value of 1+w+w^(2)+.......+w^(n-1) is :

If a=cos""(4pi)/(3)+isin""(4pi)/(3) , then the value of ((1+a)/(2))^(3n) is :

cos((11 pi)/(6))=

sin^(-1)(sin ((7pi)/6))

If a= cos((2pi)/7)+isin((2pi)/7) , alpha= a+a^2+a^4 ,and beta =a^3+a^5+a^6 then alpha ,beta are the roots of the equation

Prove that: sin ((8pi)/3) cos ((23pi)/6)+cos ((13pi)/3) sin ((35pi)/6)=1/2

Evaluate : "sin" (8 pi)/(3) "cos" (23 pi)/(6) + "cos" (13 pi)/(3) "sin" (35 pi)/(6)

Let A=[[1,1],[0,1]] and P=[[cos(pi/6),sin(pi/6)],[-sin(pi/6),cos(pi/6)]] and Q=PAP^T then P^T Q^2013 P is: