Question

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

7 tan3x - 21 tan x = 0

how do I do this?

Answer 1

at what values of x will the equations be zero?

Answer 2

7 tan^3x - 21 tanx = 0
=> 7tanx (tan^2 x - 3) = 0
=> tanx = 0 or tan^2 x = 3
=> x = 0 or π
or tanx = ± √3, i.e., tanx = √3 or tanx = - √3
tanx = √3
=> tanx = tan (π/6) or tan (π + π/6)
=> x = π/6 or 7π/6
and
tanx = - √3
=> tanx = tan (π - π/6) or tan (2π - π/6)
=> x = 5π/6 or 11π/6

Answer 3

And the Answer will be? @chris215

Answer 4

Answer: x = { 0, π/6, 5π/6, π, 7π/6, 11π/6 }.