Finding all solutions to \tan^5 x-9\tan x=0

Akbar Witt

Akbar Witt

Answered question

2022-02-27

Finding all solutions to
tan5x9tanx=0

Answer & Explanation

Randall Odom

Randall Odom

Beginner2022-02-28Added 5 answers

tan2x=3cos2x=1tan2x1+tan2x=131+3=12=cos2π3
2x=2nπ±2π3=2π3(3n±1) where n is any integer.
x=π3(3n±1)
Now, we need 0π3(3n+1)<2π03n+1<6n=0,1
For n=1,x=π3(3n1)=2π3; n=2x=π3(3n1)=5π3

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