[" The wifte "(cos2p pi+i sin2p pi)(cos2q pi+i sin2q pi)=1]

The polar form of (i^(255))^(3) is (cos pi)/(2)+i(sin pi)/(2)bcos pi+is in pi c*cos pi-i sin pi d(cos pi)/(2)-is in(pi)/(2)

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

Find the value of expression (cospi/2+i sin(pi/2))(cos(pi/(2^2))+i sin(pi/(2^2)))......oo

Evaluate the following: (cos(2 pi))/(3)(cos pi)/(4)-(sin(2 pi))/(3)(sin pi)/(4)

Simplify: [(1+ (sin pi) / (8) + i (cos pi) / (8)) / (1+ (sin pi) / (8) -i (cos pi) / (8))] ^ ((1) / (2))

Prove that (i) " tan"^(2) .(pi)/(3) + 2cos^(2) .(pi)/(4)+ 3 sec^(2).(pi)/(6)+ 4 cos^(2).(pi)/(2)=8 (ii) " sin ".(pi)/(6) " cos 0 + sin ".(pi)/(4) " cos " .(pi)(4) + " sin " .(pi)/(3) "cos " .(pi)/(6) =(7)/(4) (iii) " 4sin " (pi)/(6) " sin"^(2) (pi)/(3) + 3 " cos " .(pi)/(3) " tan ".(pi)/(4) = " cosec"^(2).(pi)/(2)=4

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

Prove that (cos (2pi r +- (pi)/4))/(sin{q pi + (-1)^q cdot (pi)/4}) = 1 where p and q are integers.

One of the values of ((cos (pi)/(6)-i sin (pi)/(6))^(1 / 2))((cos (pi)/(6)+i sin (pi)/(6))^(1 / 2)) is