Show that is an eigenvalue of the Sturm- Liouville problem

and find a corresponding eigenfunction.

To start i posed that the solution of this problem will be in the form

using the end point conditions i get

this clearly gives us...

clearly If A=B=0 this would give us a dummy answer so i toss it, and say that first this equation to be true,

Where i am stuck is when i use the second endpoint condition i get...

with substitution + algebra putting the sin on one side and the cos on the other we get...

divide both sides by cos.....

substitute,

implies

SO how do i use this to prove is an eigenvalue, then how do i find my function.... please help