By virtue of complex methods and tools, the authors express the famous Wallis formula as a sum involving binomial coefficients, establish the expansions for $\sin^kx$ and $\cos^kx$ in terms of $\cos(mx)$, find the general formulas for the derivatives of $\sin^kx$ and $\cos^kx$, and recover the general multiple-angle formulas for $\sin(kx)$ and $\cos(kx)$, where $k𝟄ℕ$ and $m𝟄ℤ$.