If ( frac{cos 5 mathrm{A}}{cos mathrm{A}}+frac{sin 5 mathrm{A}}{sin mathrm{A}} equiv mathrm{a}+mathrm{b} cos 4 mathrm{A}, ) then find the value of ( frac{(mathrm{a}+mathrm{b})}{2} )

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The value of  frac{a + b}{2} = 3

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