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De Moivre's theorem states that
(cos theta - i sin theta)^n = cos n theta + i sin n theta for n E R.
(a) Use induction to prove de Moivre's theorem for n E Z^+.
(b) Show that
cos 5 theta = 16 cos^5 theta - 20 cos^3 theta + 5 cos theta.
(c) Hence show that 2 cos pi/10 is a root of the equation
x^4 - 5x^2 + 5 = 0.© BrainMass Inc. brainmass.com March 4, 2021, 8:42 pm ad1c9bdddf
This solution illustrates how DeMoivre's theorem is applied to verifying the root of an equation. All calculations and steps are shown in the attached Word document which is attached.