+129840 cos4θ +cos6θ =0
cos4θ = cos(5θ - θ) = cos5θcosθ + sin5θsitnθ
cos6θ = cos(5θ + θ) = cos5θcosθ - sin5θsinθ
So.......
cos4θ +cos6θ = 0 → [ cos5θcosθ + sin5θsinθ ] + [cos5θcosθ - sin5θsinθ] = 0 →
2cos5θcosθ = 0 divide by 2
cos5θcosθ= 0
Set each factor to 0
cosθ = 0 at θ = pi/2 + n*pi ..... and........
cos5θ = 0 at θ = pi/10 + n*pi/5
Here's a graph of the solutions :
