Find all solutions in the interval [0, 2π).

7 tan^3x - 21 tan x = 0

A) pi/3, 2pi/3, 4pi/3, 5pi/3

B) 0, pi/5, π, 6pi/5

C) 0, pi/3, 2pi/3, π, 4pi/3, 5pi/3

D) 0, pi/3, π, 4pi/3

Question

Mathematics

Glenn Pham

Today, 02:57

Find all solutions in the interval [0, 2π).

7 tan^3x - 21 tan x = 0

A) pi/3, 2pi/3, 4pi/3, 5pi/3

B) 0, pi/5, π, 6pi/5

C) 0, pi/3, 2pi/3, π, 4pi/3, 5pi/3

D) 0, pi/3, π, 4pi/3

+3

Answers (1)

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Titus Vance · Answer 1

Let tan x = a

7 tan^3 x - 21 tan x = 0 becomes

7a^3 - 21a = 0

7a (a^2 - 3) = 0

a = 0 or a^2 - 3 = 0

a = 0 or a^2 = 3

a = 0 or a = + or - √3

tan x = 0, tan x = √3, tan x = - √3

x = 0, pi, pi/3, 4pi/3, 2pi/3, 5pi/3

Find all solutions in the interval [0, 2π).7 tan^3x - 21 tan x = 0A) pi/3, 2pi/3, 4pi/3, 5pi/3B) 0, pi/5, π, 6pi/5C) 0, pi/3, 2pi/3, π, 4pi/3, 5pi/3D) 0, pi/3, π, 4pi/3

Find all solutions in the interval [0, 2π).

7 tan^3x - 21 tan x = 0

A) pi/3, 2pi/3, 4pi/3, 5pi/3

B) 0, pi/5, π, 6pi/5

C) 0, pi/3, 2pi/3, π, 4pi/3, 5pi/3

D) 0, pi/3, π, 4pi/3