Let A be the matrix given in the question.
Now,Trace(A)=sum of eigen values of A
or,Trace(A)=cos α + cos α=2*cos α
Now,by adding and subtracting sin α we get:
or,2cos α=(cos α + sin α) + (cos α - sin α)= λ1 + λ 2
Therefore, 2 eigen values can be denoted by (cos ∝ ± sin ∝ (d))
So, Option (d) is the ans.