Question

ayúdenme resolviendo estos dos ejercicios les doy 50pts

tan x + sen x = 0

tan x - sen 2x = 0

Answer 1

Tarea

Resolver:

a)  tan x + sen x = 0

b)  tan x - sen 2x = 0

Hola!!!

a)

tan x + sen x = 0

Sabemos que: Tang x = Senx/Cosx

Senx/Cosx + Senx = 0

Sex/Cosx = -Senx

Senx = -Senx × Cosx

Senx/-Senx = Cosx

Cosx = -1  ⇒

x = Cos⁻¹ (-1)

x = 180° = π

b)

tan x - sen 2x = 0

Sabemos que: Sen2x = 2Senx × Cosx

Senx/Cosx - 2Senx × Cosx

Senx/Cosx = 2Senx × Cosx

Senx/2Senx = Cosx × Cosx

1/2 = Cos²x

Cosx = ±√1/2 ⇒

Cosx = +√1/2    

Cosx = 1/√2  ⇒

x = Cos⁻¹ (1/√2)  

x = 45° = π/4

Cosx = -√1/2

Cosx = -1/√2  ⇒

x = Cos⁻¹ (-1/√2)

Sabemos que: π = 180°  ⇒

135° × π/180° = 3/4π

x = 135° = 3/4π

Saludos!!!