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Home » The LCM takes the highest powers of all primes: - High Altitude Science

The LCM takes the highest powers of all primes: - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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3(1 - 2d) - d = 3 - 6d - d = 3 - 7d = -2 \Rightarrow 7d = 5 \Rightarro...
\mathbf{M} = egin{bmatrix} 2 & 1 \ -rac{3}{7} & rac{5}{7} \end{bmat...
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 + \...
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)} +...
But better: use identity:
an x + \cot x = rac{\sin x}{\cos x} + rac{\cos x}{\sin x} = rac{\si...
Now the full expression:

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