Hello :
by idetity : 1+cos(2a) = 2cos²(a)
let : a = <span>θ/2
1+cos(2×</span>θ/2)=2cos²(θ/2)
1+cos(θ) = 2cos²(θ/2)
solve : 2 cos^2 (θ/2) - 3 cos(θ) = 0 ......(1)
(1) : 1+cos(θ)-3 cos(θ) =0
2cos(θ) = 1
cos(θ) = 1/2
in : [0, 2π<span>[
</span>( θ = π/3) or (θ = 5π/3)
<span>11.00001 - 1.11234</span> = 9.88767
The larger number is 51 and the smaller number is 12. ( hope I helped) have a good day
