Its just this Bill - since the eigenvalue equaiton is redundant, you can go ahead and specify either a or b as long as the normalization condition is still satisfied.
So, since its a free parameter, you set a equal to the expected solution eigenket, a=cos beta
Then you solve for b.
Homework Statement
http://www.ocf.berkeley.edu/~yayhdapu/postings/sak19.gif
Homework Equations
The Attempt at a Solution
http://www.ocf.berkeley.edu/~yayhdapu/postings/sakurai1.9.pdf"
http://www.ocf.berkeley.edu/~yayhdapu/postings/sakurai1.9.docx"
These are here in this attached...