Solve \(\displaystyle{\tan{{\left(\theta\right)}}}+{\tan{{\left({2}\theta\right)}}}={\tan{{\left({3}\theta\right)}}}\)

sexoagotadorogyr

sexoagotadorogyr

Answered question

2022-03-20

Solve tan(θ)+tan(2θ)=tan(3θ)

Answer & Explanation

Declan Cameron

Declan Cameron

Beginner2022-03-21Added 12 answers

tan(θ)+tan(2θ)=tan(3θ)
tan(θ)+tan(2θ)=tan(θ+2θ)
tan(θ)+tan(2θ)1=tan(θ)+tan(2θ)1tan(θ)tan(2θ)
So, either tan(θ)+tan(2θ)=0 or tan(θ)=0 or tan(2θ)=0
tan(θ)+tan(2θ)=0
tan(θ)+2tan(θ)1tan2(θ)=0
3tan(θ)tan3(θ)=0
tan(θ){0,±3}
So θ{nπ,±13π+nπ,±14π+nπ:nZ}

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