Question

Si:tgx ctg 3y=1 sen y=cos70° calcular tgx

Answer 1

Respuesta:

tg x = √3

Explicación paso a paso:

tg x . ctg 3y = 1

tg x = 1 / ctg 3y

tg x = tg 3y

x = 3y

sen y = cos 70°

El ángulo complementario a 70° es 20°

Utilizar:  cos 70° = sen 20°

sen y = sen 20°

y = 20°

x = 3y

x = 3(20°)

x = 60°

tg x = tg 60°

Utilizar triangulo notable de 30°, 60°:

Cateto menor = 1

Cateto mayor = √3

Hipotenusa = 2

tg 60° = Cateto mayor / Cateto menor

tg 60° = √3 / 1

tg 60° = √3

tg x = tg 60°

tg x = √3