Question

Answer 1

\(2+2cosx=2\left(1+cosx\right)=2\left(1+2cos^2\dfrac{x}{2}-1\right)=4cos^2\dfrac{x}{2}\)

\(\Rightarrow\sqrt{2+2cosx}=2cos\dfrac{x}{2}=2cos\dfrac{x}{2^1}\) (1 dấu căn)

\(\Rightarrow\sqrt{2+\sqrt{2+2cosx}}=\sqrt{2+2cos\dfrac{x}{2}}=2cos\dfrac{x}{4}=2cos\dfrac{x}{2^2}\) (2 dấu căn)

Từ đó ta có: \(P=2cos\dfrac{x}{2^{2020}}\)