Question

If, tan theta + tan 2 theta - tan 3 theta = 0, then find theta?

Answer 1

Answer:

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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