The number of solutions of equation `tan^(-1)2x+tan^(-1)3x=pi/4` is (a) 2 (b) 3 (c) 1 (d) none of these

Explanation

To solve the equation \( \tan^{-1}(2x) + \tan^{-1}(3x) = \frac{\pi}{4} \), we can use the formula for the sum of inverse tangents:

\[ \tan^{-1}(a) + \tan^{-1}(b) = \tan^{-1}\left(\frac{a + b}{1 - ab}\right) \]

where \( a = 2x \) and \( b = 3x \).

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