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Home » \cos(lpha - (90^\circ - lpha)) = \cos(2lpha - 90^\circ) = rac13. - AMAZONAWS

\cos(lpha - (90^\circ - lpha)) = \cos(2lpha - 90^\circ) = rac13. - AMAZONAWS

📅 March 11, 2026 👤 scraface
Mar 11, 2026
\cos(lpha - (90^\circ - lpha)) = \cos(2lpha - 90^\circ) = rac{1}{3}.

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📌 Lösung: Eine Zahl, die durch beide teilbar ist, muss durch ihr kleinstes gemeinsames Vielfaches teilbar sein. Berechnen: \( \text{lcm}(12, 18) \). Primfaktorzerlegung: \( 12 = 2^2 \cdot 3 \), \( 18 = 2 \cdot 3^2 \) → \( \text{lcm} = 2^2 \cdot 3^2 = 36 \). Wir suchen die kleinste vierstellige Zahl, die durch 36 teilbar ist. Die kleinste vierstellige Zahl ist 1000. Teilen: \( 1000 \div 36 \approx 27.78 \). Die kleinste ganze Zahl \( k \) mit \( 36k \ge 1000 \) ist \( k = 28 \). Dann \( 36 \times 28 = 1008 \). Überprüfen: \( 1008 \ge 1000 \), und \( 1008 \div 36 = 28 \), also teilbar. Somit ist die kleinste vierstellige Zahl, die durch beide teilbar ist, \( \boxed{1008} \).
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