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u_n chỉ có 1 số hạng nhận giá trị nguyên.

Chưa chuẩn bạn nhé.

\(4sin^2x+8tan^2x=4\left(1-cos^2x\right)+\dfrac{8sin^2x}{cos^2x}\\ =4\left(1-cos^2x\right)+\dfrac{8\left(1-cos^2x\right)}{cos^2x}=4\left[1-\left(-\dfrac{1}{2}\right)^2\right]+\dfrac{8\left[1-\left(-\dfrac{1}{2}\right)^2\right]}{\left(-\dfrac{1}{2}\right)^2}=27\)

\(sin(\dfrac{\pi}{2}-x)cot(\pi+x)=cosxcotx=\dfrac{cosx}{tanx}\\ =\dfrac{\dfrac{1}{\sqrt5}}{-2}=\dfrac{-\sqrt5}{10}\)

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\(\omega=\dfrac{2\pi}{T}=\dfrac{2\pi}{1}=2\pi\left(\dfrac{rad}{s}\right)\\ v_{max}=\omega A=2\pi.4=8\pi\left(\dfrac{cm}{s}\right)\\ \varphi_v=\dfrac{\pi}{2}\\ \rightarrow v=8\pi cos\left(2\pi t+\dfrac{\pi}{2}\right)\)

\(v=\pm\omega\sqrt{A^2-x^2}=\pm5\pi\sqrt{10^2-8^2}=\pm30\pi\left(\dfrac{cm}{s}\right)\)