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Home » "OMG—This Camo Hooded Sweatshirt for Women Disrupts Every Fashion Trend This Season! - 500apps

"OMG—This Camo Hooded Sweatshirt for Women Disrupts Every Fashion Trend This Season! - 500apps

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 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:

📌 an x + \cot x = rac{\sin x}{\cos x} + rac{\cos x}{\sin x} = rac{\sin^2 x + \cos^2 x}{\sin x \cos x} = rac{1}{\sin x \cos x} = rac{2}{\sin 2x}

📌 Now the full expression:

📌 + \sin 2x + rac{4}{\sin^2 2x}

📌 Let \(t = \sin 2x\), \(0 < t \leq 1\) (since \(x \in (0, \pi/2)\Rightarrow 2x \in (0, \pi)\), and \(t = 1\) at \(x = \pi/4\))

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Now compute \(3025 \mod 11\). First, reduce 55 modulo 11:
\(55 \div 11 = 5\), so \(55 \equiv 0 \pmod{11}\).
Then \(55^2 \equiv 0^2 = 0 \pmod{11}\).
Thus, \(3025 \equiv 0 \pmod{11}\).
Alternatively, since \(55 \equiv 0 \mod 11\), the square is divisible...
Therefore, the remainder is \(\boxed{0}\).
An emerging technology researcher exploring base systems in quantum co...
To convert \(321_9\) to base ten, expand using powers of 9:
321_9 = 3 \times 9^2 + 2 \times 9^1 + 1 \times 9^0
\times 81 = 243, \quad 2 \times 9 = 18, \quad 1 \times 1 = 1

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