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30 July, 13:28

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

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Answers (1)
  1. 30 July, 13:47
    0
    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
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