If `A=[[cos(2 pi/33),sin(2 pi/33)],[-sin(2 pi/33),cos(2 pi/33)]]`, then `A^2007` is

A=[[cos((2 pi)/(33)),sin((2 pi)/(33))],[-sin((2 pi)/(33)),cos((2 pi)/(33))]] , then A^(2017)=

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

sin(pi/4+A).sin(pi/4-A)=1/2 cos2A

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

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

|[1,(3 pi)/(10),(2 pi)/(10)],[0,cos(3 pi)/(10),sin(2 pi)/(10)],[0,sin(3 pi)/(10),cos(2 pi)/(10)]|

The value of the determinant |sin theta,cos theta,sin2 thetasin(theta+(2 pi)/(3)),cos(theta+(2 pi)/(3)),sin(2 theta+(4 pi)/(3))sin(theta-(2 pi)/(3)),cos(theta-(2 pi)/(3)),sin(2 theta-(4 pi)/(3))

sin pi/3 = 2sin pi/6 cos pi/6