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Home » rac1k(k+2) = rac12\left( rac1k - rac1k+2 - AMAZONAWS

rac1k(k+2) = rac12\left( rac1k - rac1k+2 - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 3(1 - 2d) - d = 3 - 6d - d = 3 - 7d = -2 \Rightarrow 7d = 5 \Rightarrow d = rac{5}{7},\ c = 1 - rac{10}{7} = -rac{3}{7}

📌 \mathbf{M} = egin{bmatrix} 2 & 1 \ -rac{3}{7} & rac{5}{7} \end{bmatrix}

📌 oxed{egin{bmatrix} 2 & 1 \ -\dfrac{3}{7} & \dfrac{5}{7} \end{bmatrix}}

📌 Question: Find the maximum value of \((\sin x + \cos x)^2 + ( an x + \cot x)^2\) for \(0 < x < rac{\pi}{2}\).

📌 Solution: First, expand:

📌 Let \(u = \sin^2 x\), then \(\cos^2 x = 1 - u\), so:

📌 rac{u}{1 - u} + rac{1 - u}{u} + 2 = rac{u^2 + (1 - u)^2}{u(1 - u)} + 2 = rac{u^2 + 1 - 2u + u^2}{u(1 - u)} + 2 = rac{2u^2 - 2u + 1}{u(1 - u)} + 2

📌 But better: use identity:

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