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📅 May 1, 2026 👤 scraface

May 01, 2026

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🔥 Popular Posts

Among any three consecutive integers, one must be divisible by 2 (sinc...
Among any three consecutive integers, one must be divisible by 3 (sinc...
Thus, the product \( n(n+1)(n+2) \) is divisible by both 2 and 3. Ther...
Additionally, consider the divisibility by 4. Among any three consecut...
Therefore, the product \( n(n+1)(n+2) \) is divisible by the least com...
\text{lcm}(4, 3) = 12
We can confirm this by testing specific cases (like 1, 2, 3 or 2, 3, 4...
Thus, the largest integer that must divide the product of any three co...
How many lattice points lie on the line segment joining (1, 2) and (7,...
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📝 Recent Posts

\sec^2 x + \csc^2 x = \frac{1}{\cos^2 x} + \frac{1}{\sin^2 x} = \frac{...
Also, $\sec x \csc x = \frac{1}{\sin x \cos x}$, so:
2\sec x \csc x = \frac{2}{\sin x \cos x}
And $2\sin x \cos x$ remains.
Let $u = \sin x \cos x$. Since $x \in (0, \frac{\pi}{2})$, $u > 0$, an...
Now rewrite the entire expression in terms of $u$:
\frac{1}{u^2} + \frac{2}{u} + 1 + 2u
Define the function:
f(u) = \frac{1}{u^2} + \frac{2}{u} + 1 + 2u, \quad 0 < u \leq \frac{1}...
We now find the maximum of $f(u)$ on this interval. Note that as $u \t...

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