Another De Moivre's & Trig Question (1 Viewer)

[pixiefeathers]

Hi, for part b of this question (Cambridge Exercise 3F Q12), I solved up to the part where θ = π/2, 3π/2, etc, following the attached solution below. I understand that you need to omit the root of cosθ=0 from the roots of cos5θ to get the required roots, but cosθ=0 would happen for all π/2, 3π/2, etc, so why is it π/2 the specific solution omitted?

 

[tywebb]

0 is a solution to 16x⁵-20x³+5x=0 but not to 16x⁴-20x²+5=0

cos(π/2) = 0 came about as a solution to 16x⁵-20x³+5x=0

Whether you express 0 as cos(π/2), cos(3π/2), etc., doesn't matter. They all have to be excluded as solutions to 16x⁴-20x²+5=0.

 

[pixiefeathers]

Ohh right, ok I get it now, thank you so much.