Question

Sejam a,b ∈ (0, π/2), tais que, sen a=2/3 e cosb=3/5. Podemos concluir que cos(a+b)=?
SOCORRO

Answer 1

Resposta:

Explicação passo a passo:

sen a=2/3

$sen^2a+cos^2a=1\\(\frac{2}{3} )^2+cos^2a=1\\\frac{4}{9}+cos^2a=1\\cos^2a=1-\frac{4}{9} \\cos^2a=\frac{5}{9} \\cosa=\sqrt{\frac{5}{9} } \\cosa = \frac{\sqrt{5} }{3}$

cosb=3/5

$sen^2b+cos^2b=1\\sen^2b + (\frac{3}{5})^2 = 1\\ sen^2b + \frac{9}{25} = 1\\sen^2b = 1-\frac{9}{25}\\sen^2b = \frac{16}{25} \\senb=\sqrt{ \frac{16}{25} }\\senb = \frac{4}{5}$

Cosseno da soma:

cos(a + b) = cos a.cos b - sen a.sen b

$cos(a+b)=\frac{\sqrt{5} }{3} *\frac{3}{5} -\frac{2}{3}*\frac{4}{5} \\\\cos(a+b)=\frac{\sqrt{5} }{5} -\frac{8}{15} \\\\cos(a+b)=\frac{3\sqrt{5}-8 }{15}$