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Question

The general value of θ satisfying equation tan3θtan2θtanθ=0

A
nπ
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B
nπ4
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C
nπ2
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D
nπ3
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Solution

The correct option is D nπ3
As 2θ+θ=3θtan(2θ+θ)=tan3θ

tan2θ+tanθ1tan2θtanθ=tan3θ

tan2θ+tanθ=tan3θtanθtan2θtan3θtan3θtan2θtanθ=tanθtan2θtan3θ

Now
tan3θtan2θtanθ=0tanθtan2θtan3θ=0

θ=nπ or 2θ=nπ or 3θ=nπ

θ=nπ3

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