Question

Si tan(x+y)=1/2; tan(z-x)=1/3.
Calcular tan(y+z)

Con procedimiento, por favor :(

Answer 1

El valor de la Tan(y + z) es:

Tan(y + z) = 1

Si Tan(x + y) = 1/2; Tan(z - x) = 1/3;

Aplicar trigonometria para resolver el problema.

Tan(α) = Cat. Op/Cat. Ady

Aplicar inversa;

α = Tan⁻¹(Cat. Op/Cat. Ady)

Tan(x + y) = 1/2

Aplicar inversa;

(x + y) = Tan⁻¹(1/2)

Tan(z - x) = 1/3

Aplicar inversa;

(z - x) = Tan⁻¹(1/3)

Despejar x;

x = z - Tan⁻¹(1/3)

Sustituir;

z - Tan⁻¹(1/3) + y = Tan⁻¹(1/2)

y + z = Tan⁻¹(1/2) + Tan⁻¹(1/3)

y + z = 45°

Tan(45°) = 1

Tan(y + z) = 1