Question

Tantheta +tan2theta +tn3theta =0 general solution

Answer 1

Answer:

tanθ+tan2θ+tan(θ+2θ)=0

(tanθ+tan2θ)+  

1−tanθtan2θ

tanθ+tan2θ

​  

=0

(tanθ+tan2θ)(1−tanθtan2θ+1)=0

tan2θ+tanθ=0

∴tan2θ=−tanθ=tan(−θ)

∴2θ=nπ−θ or 3θ=nπ

∴θ=nπ/3

From 2nd factor

tanθtan2θ=2 or tanθ⋅  

1−tan  

2

θ

2tanθ

​  

=2

tan  

2

θ=1−tan  

2

θ or 2tan  

2

θ=1

∴tanθ=±  

(2)

​  

 

1

​  

=±tanα where tanα=  

(2)

​  

 

1

​  

 

∴θ=nπ±α where α=tan  

−1

 

(2)

​  

 

1

​  

 

0<α<π/2

Step-by-step explanation:

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