We know that-

2 cos x cos y = cos(x + y) + cos(x - y)

Putting x = (9π/13) and y = (π/13) in (1), we get-

…(1)

∴ L.H.S

[From (1)]

since cos (π/2) = 0

∴ L.H.S = 0 + 0 = 0 = R.H.S

Hence, L.H.S = R.H.S…Proved