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General Solution of a Differential Equation

Solve tan 3...

Question

Solve $\frac{t a n 3 x - t a n 2 x}{1 + t a n 3 x t a n 2 x} = 1$

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Solution

L.H.S. $= t a n (3 x - 2 x) = t a n x = 1$ Therefor, $x = n π + (π / 4), n \in Z .$ but these values does not define $t a n 2 x$ . Hence, there is no solution.

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