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Sin alfa+cos alfa=2/5. Calculati sin de 2alfa. Multumesc!

Răspuns :

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Vezi imaginea GEORGE100007

sin alfa+cos alfa=2/5 |()^2=>sin^2 alfa+cos^2 alfa+2sin alfa •cos alfa=4/25 (1)

Formula fundamentala a trigonometriei:sin^2 alfa+ cos^2 alfa=1 (2)

Inlocuim relatia(2) in relatia (1) si obtinem 1+2sin alfa •cos alfa=4/25<=>2sin alfa •cos alfa=-21/25=>sin2alfa=-21/25