Find modulus and argument for `z = 1-sin alpha + i cos alpha`, `alpha in (0,2pi)`

If (3pi)/(2) lt alpha lt 2 pi , find the modulus and argument of (1 - cos 2 alpha) + i sin 2 alpha .

If (3pi)/(2) gt alpha gt 2 pi , find the modulus and argument of (1 - cos 2 alpha) + i sin 2 alpha .

If (pi)/(2) lt alpha lt (3pi)/(2) , the modulus and argument form of (1+cos2alpha)+isin2alpha is

If (pi)/(2) lt alpha (3pi)/(2) , the modulus argument form of (1 + cos 2 alpha) + isin 2 alpha is

Find |A| , if A =[{:( 0 , sin alpha , cos alpha),(sin alpha , 0 , sin beta),(cos alpha , -sin beta , 0):}]

Find inverse of the matrix A=[[cos alpha, -sin alpha, 0 ],[ sin alpha, cos alpha, 0],[ 0, 0, 1]]

If pi/2

If alpha-beta=(2n+1)(pi)/2, n epsilon Z then [(cos^(2) alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)][(cos^(2) beta, cos beta sin beta),(cos beta sin beta, sin^(2) beta)]=