Question

Simplifica la expresión: [tg(x)cos(x)]² + [ctg(x)sen(x)]²
1
3
sen(x)
cos(x)

Answer 1

Respuesta:

Explicación paso a paso:

Para resolver aplicamos las fórmulas trigonométricas:

$tg(x)= \frac{sen(x)}{cos(x)} , \\ ctg(x)= \frac{cos(x)}{sen(x)},\\ y\\sen^{2} (x)+cos^{2} (x)=1$

[tg(x)cos(x)]² + [ctg(x)sen(x)]²=  

$tg^{2}(x)cos^{2}(x)+ ctg^{2}(x)sen^{2}(x)=\\\\ \frac{sen^{2} (x)}{cos^{2} (x)} . cos^{2}( x)+ \frac{cos^{2} (x)}{sen^{2} (x)} .sen^{2} (x)=\\\\cos^{2}( x)+sen^{2} (x) =1$

solución :  1