sin–1 (1 – x) – 2 sin–1 x = pi/2, then x is equal to ______.

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sin–1 (1 – x) – 2 sin–1 x = pi/2, then x is equal to 0. Explanation: `sin^-1 (1 - x) - 2 sin^-1 x = pi/2 $\Rightarrow$ sin^-1 (1 - x) = pi/2 + 2 sin^-1 x` $\Rightarrow$ 1 – x = cos[cos–1 (1 – 2x2)] $\Rightarrow$ 1 – x = 1 – 2x2 $\Rightarrow$ 2x2 – x = 0 $\Rightarrow$ x = 0, $\frac{1}{2}$ But x = $\frac{1}{2}$ does not satisfy the equation. So, x = 0.

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