The general value of x satisfying tan x tan 2x = 1 is ______________.

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Solution

tan x tan 2x = 1
i.e 1 − tan x tan 2x = 0 ...(1)
$\begin{array}{rcl} Since \tan 3 x & = & \tan (x + 2 x) \\ = & \frac{\tan x + \tan 2 x}{1 - \tan x \tan 2 x} \end{array}$
i.e tan 3x = ∞ ...(from 1)
i.e 3x = $n π + \frac{π}{2}$
$i . e x = \frac{n π}{3} + \frac{π}{6}$

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