Prove that `cos(pi/12)+cos(3pi/12)+cos(9pi/12)+cos(11pi/12)=0`

cos^2(pi/12)+cos^2(pi/4)+cos^2((5pi)/12)=

cos(pi/7)cos((2pi)/7)cos((4pi)/7)=

cos(pi/5)cos((2pi)/5)cos((4pi)/5)cos((8pi)/5)=

Prove the following: cos(pi/2-x)cos(pi/2-y)-sin(pi/2-x)sin(pi/2-y)=-cos(x+y)

Prove cos2pi/15cos4pi/15cos8pi/15cos16pi/15=1/16

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

The value of cos""(pi)/(11)+cos""(3pi)/(11)+cos""(5pi)/(11)+cos""(7pi)/(11)+cos""(9pi)/(11), is

Prove that (i) " 2sin " (5pi)/(12) " sin " (pi)/(12)=(1)/(2) (ii) " 2 cos " (5pi)/(12) " cos " .(pi)/(12)=(1)/(2) (iii) " 2 sin ".(5pi)/(12) " cos " (pi)/(2) = ((2+sqrt(3))/(2))

cos ""(2pi)/( 15) cos ""(4pi)/(15) cos ""(8pi)/(15) cos ""(16pi)/(15)=