Two functions too trouble

Geometry Level 4

Let \(f(x) = 2(a-x)(x+\sqrt{x^{2}+9})\) and \(g(y) = 9+7\cos ^{2} x + 24\sin x \cos x\) be two functions having same maximum value.That is, \(f_\text{max} = g_\text{max}\).

Given that \(a>0\),find the value of \(a\).

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