The number of solutions of the equation t a n - 1 x 1 - x 2 + t a n - 1 1 x 3 = 3 π 4 belonging to the interval 0 ,    1 is

Question

The number of solutions of the equation t a n - 1 x 1 - x 2 + t a n - 1 1 x 3 = 3 &#960; 4 belonging to the interval 0 , &#8201;&#8201; 1 is

Aicharya · Accepted Answer

$ x \in (0, 1) \Rightarrow \frac{x}{1-x^2} > 0 ; \frac{1}{x^3} > 0 \Rightarrow \frac{x}{1-x^2} \cdot \frac{1}{x^3} > 1 $ $ 	an^{-1}\left(\frac{x}{1-x^2}ight) + 	an^{-1}\left(\frac{1}{x^3}ight) = \pi + 	an^{-1}\left|\frac{\frac{x}{1-x^2} + \frac{1}{x^3}}{1 - \frac{x}{1-x^2} \cdot \frac{1}{x^3}}ight| = \pi + 	an^{-1}\left|\frac{-1}{x}ight| = \frac{3\pi}{4} $ $ \Rightarrow x = 1 $ (not possible)

The number of solutions of the equation t a n - 1 x 1 - x 2 + t a n - 1 1 x 3 = 3 π 4 belonging to the…

Solution

The number of solutions of the equation t a n - 1 x 1 - x 2 + t a n - 1 1 x 3 = 3 &#960; 4 belonging to the…

Solution

The number of solutions of the equation t a n - 1 x 1 - x 2 + t a n - 1 1 x 3 = 3 π 4 belonging to the…