If sec(a-b),seca and sec(a+b) are in AP find cos a in terms of b

We can write:

2sec a = sec(a – b) + sec(a+b)
or 2cos(a-b)cos(a+b) = cosa [ cos(a-b) + cos(a+b)]
on further simplification,
2(cos^2a – sin^2a) = 2cos^acos b
finally, we can simplify here to get the value of cos a in terms of b
cosa = sinb/(sqrt(1 – cos B))