(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 (cospi/2+i sin(pi/2))(cos(pi/(2^2))+i sin(pi/(2^2)))......oo

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

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

The polar form of (i^(25))^3 is a. cos(pi/2)+isin(pi/2) b. cospi+i\ sinpi c. cospi-isinpi d. cos(pi/2)-\ i sin(pi/2)

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))

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))

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

(1+sin phi+i cos phi)/((1+sin phi-i cos phi)^(n))=cos(n(pi)/(2)-n phi)+i sin(n(pi) /(2)-n phi)

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