Help!!

take x₀ = Cos(θ)
and try to solve it . u get a pattern like this,
x₁ = Cos(θ/2)
x₂ = Cos(θ/2²)....and so on
...
x_n = Cos(θ/2ⁿ)

now u get a value of

x₁.x₂.x₃......x_n = Cos(θ/2).Cos(θ/2²)........Cos(θ/2ⁿ)

now multiply and divide by Sin(θ/2ⁿ)

on solving u get,

x₁.x₂.x₃......x_n = (1/2)ⁿSin(θ)/Sin(θ/2ⁿ)

uget the value of ,
y = (√1-x₀²)/x₁.x₂.x₃......x_n = 2ⁿ.Sin(θ/2ⁿ)

on taking limt as n→∞

we get
y = θ

now Cos (y) = Cos (θ)
= x₀
so final answer will be x₀