If $tan 4 x + tan 5 x - tan 9 x = k tan 4 x tan 5 x tan 9 x$ then $k =$

1

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- 1

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\pm 1

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Solution

The correct option is A $- 1$
$\begin{matrix} tan 9 x = tan (4 x + 5 x) = \frac{tan 4 x + tan 5 x}{1 - tan 4 x tan 5 x} \Rightarrow tan 9 x - tan 4 x tan 5 x tan 9 x = tan 4 x + tan 5 x \Rightarrow tan 4 x + tan 5 x - tan 9 x = - tan 4 x tan 5 x tan 9 x ∴ k = - 1 \end{matrix}$

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