find the general solution
of tan ^3 x-tan 3 x=0
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Step-by-step explanation:
tan ^3 x-tan 3 x=0
let tan x = t
t³ - ( 3t -t³) / 1-3t² = 0
t³ - t( 3 -t²) / 1-3t² = 0
t { t² - ( 3 -t²) / 1-3t² } = 0
t { t²(1-3t²) - ( 3 -t²) } = 0
t { t²-3t∧4 - 3 +t²) } = 0
t { 3t∧4 -2t² + 3 } = 0
t ( t²-1) ( t² - 1/3) = 0
t = 0 , ±1 , ±1/√3
t = 0 : x = 0, π , 2π , ... = nπ , n integer≥0
t = ±1 : x = nπ/4 , n integer ≠0
t = ±1/√3 : x = nπ/6 , n integer ≠0
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