`A=[(cos alpha,-sin alpha),(sin alpha,cos alpha)]` and `A+A^(T)=I`, find the value of `alpha`.

Explanation

`A=[(cos alpha, -sin alpha),(sin alpha, cos alpha)]`
`implies A^(T)=[(cos alpha, sin alpha),(-sin alpha, cos alpha)]`
Now, `A+A^(T)=I`
`:. [(cos alpha, -sin alpha),(sin alpha, cos alpha)]+[(cos alpha, sin alpha),(-sin alpha, cos alpha)]=[(1,0),(0,1)]`
`implies [(2 cos alpha,0),(0, 2 cos alpha)]=[(1,0),(0,1)]`
Comparing the corresponding elements of the two matrices, we have
`2 cos alpha=1`
or `cos alpha=1/2 ="cos" pi/3`
`:. alpha=2n pi pm pi/3, n in Z`