`cos((2pi)/3)-sin((2pi)/3)=?`

sin((13pi)/3)sin((8pi)/3)+cos((2pi)/3)sin((5pi)/6)=1/2

Let omega be the complex number cos((2 pi)/(3))+i sin((2 pi)/(3))* Then the number of distinct complex cos numbers z satisfying Delta=det[[omega,z+omega^(2),1omega,z+omega^(2),1omega^(2),1,z+omega]]=0 is

sin((pi)/(3)+A).cos((pi)/(3)+B)-cos((pi)/(3)+A).sin((pi)/(3)+B)=...

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

Prove that (a) sin^(2)(pi/6) + cos^(2)( pi/3) - tan^(2)(pi/4) = -1/2 (b) sin((8pi)/3) cos((23pi)/6) + cos((13pi)/3) sin((35pi)/6) = 1/2

If z_(1)=sqrt(2)((cos pi)/(4)+i sin((pi)/(4))) and z_(2)=sqrt(3)((cos pi)/(3)+i sin((pi)/(3))) then |z_(1)z_(2)|=

cos((pi)/(7))*cos(2(pi)/(7))*cos(10(pi)/(7))-sin((pi)/(14))*sin(3( pi)/(14))*sin(5(pi)/(14)) Find value.

What is the value of cos^(-1)(cos(2pi)/3)+sin^(-1)(sin(2pi)/3) ?