Question

Qual a soma s=sen^2 10° + sen^2 20° + sen^2 30° + ... + sen^2 90°

Answer 1

Resposta:

Explicação passo-a-passo:

$sen(90-x)=sen90.cosx-senx.cos90\\\\sen(90-x)=1.cosx-senx.0\\\\sen(90-x)=cosx\\\\sen^{2}(90-x)=cos^{2}x\\\\Assim\\\\sen^{2}10+sen^{2}80=sen^{2}10+cos^{2}10=1\\\\sen^{2}20+sen^{2}70=sen^{2}20+cos^{2}20=1\\\\sen^{2}30+sen^{2}60=sen^{2}30+cos^{2}30=1\\\\sen^{2}40+sen^{2}50=sen^{2}40+cos^{2}40=1\\\\sen^{2} 90=1\\\\somando\\\\s=1+1+1+1+1\\\\\boxed{\boxed{s=5}}$