Chebyshev Polynomial Practice: Product

Algebra Level 3

Evaluate

cos(10)cos(20)cos(30)cos(40)cos(50)cos(60)cos(70)cos(80)\cos(10^{\circ})\cos(20^{\circ})\cos(30^{\circ})\cos(40^{\circ})\cos(50^{\circ})\cos(60^{\circ})\cos(70^{\circ})\cos(80^{\circ})

If the answer can be expressed as ab\dfrac{a}{b}

Find a+ba+b

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