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The sum of all possible value of x satisfying the equation $\sin^{- 1} (3 x - 4 x^{3}) + \cos^{- 1} (4 x^{3} - 3 x) = \frac{π}{2}$ is

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Detailed Solution

$\sin^{- 1} (3 x - 4 x^{3}) + \cos^{- 1} (4 x^{3} - 3 x) = \frac{π}{2}$

$\Rightarrow 3 x - 4 x^{3} = 4 x^{3} - 3 x$

$\Rightarrow 8 x^{3} - 6 x = 0$

$\Rightarrow 2 x (4 x^{2} - 3) = 0$

$\Rightarrow x = 0, x = \pm \frac{\sqrt{3}}{2}$ .

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