Question

un favor ayuda es urgente ayudaaaaa​

Answer 1

Respuesta:

$c) Tan(2^{o})$

Explicación paso a paso:

$E=\frac{cos(10^{o})-cos(6^{o})}{-2sen(8^{o})cos(2^{o})}$

Por la identidad:

$cos(a)-cos(b)=-2sen(\frac{a+b}{2})sen(\frac{a-b}{2})$

Entonces:

$E=\frac{-2sen(\frac{10^{o}+6^{o}}{2})sen(\frac{10^{o}-6^{o}}{2})}{-2sen(8^{o})cos(2^{o})}\\\\E=\frac{-2sen(\frac{16^{o}}{2})sen(\frac{4^{o}}{2})}{-2sen(8^{o})cos(2^{o})} \\\\E=\frac{-2sen(8^{o})sen(2^{o})}{-2sen(8^{o})cos(2^{o})}$  Simplificamos:

$E=\frac{sen(2^{o})}{cos(2^{o})}$  

Por identidad:

$\frac{senx}{cosx} =tanx$

Entonces:

$E = tan(2^{o})$