Use de Moivre 's theorem to express cot 7 in terms of cot (Use the equation cot 7 0 to show that the roots of the equation x 6 21x 4 35x 2 7 0 are cot (1 14 k) for k 1, 3, 5, 9, 11, 13 and deduce that cot ) n cot 14 3 cot2 14 5 n) 7 14...

De Moivres theorem states that for any complex number z rcos i sin and any positive integer n the nth power of z can be expressed as zn rn cos n i sin ...

Use de Moivre's theorem to express cot 7 in terms of cot . (Use the equation cot

Question:

Use de Moivre's theorem to express cot 7θ in terms of cot θ.

(Use the equation cot 7θ = 0 to show that the roots of the equation x⁶ - 21x⁴ + 35x² - 7 = 0 are cot (1/14 kπ) for k = 1, 3, 5, 9, 11, 13 and deduce that