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3tan ^3(A)-tan (A)=0, A\in [0, 360]

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3tan³(A)−tan(A)=0, 0^◦≤ A≤ 360^◦

Solution

A=0, A=180^◦, A=360^◦, A=150^◦, A=330^◦, A=30^◦, A=210^◦

Radians

A=0, A=π, A=2π, A=5π6 , A=11π6 , A=π6 , A=7π6

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Solution steps

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3tan³(A)−tan(A)=0, 0^◦≤ A≤ 360^◦

Solve by substitution

tan(A)=0, tan(A)=−√33 , tan(A)=√33

tan(A)=0, 0≤ A≤ 360^◦ : A=0, A=180^◦, A=360^◦

tan(A)=−√33 , 0≤ A≤ 360^◦ : A=150^◦, A=330^◦

tan(A)=√33 , 0≤ A≤ 360^◦ : A=30^◦, A=210^◦

Combine all the solutions

A=0, A=180^◦, A=360^◦, A=150^◦, A=330^◦, A=30^◦, A=210^◦

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3tan ^3(A)-tan (A)=0, A\in [0, 360]

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