Question

sin^-1x+sin^-12x=π/2

Answer 1

this is one approach
${sin}^{ - 1} x + {sin}^{ - 1} 2x = \frac{\pi}{2} \\ we \: know \: \\ {sin}^{ - 1} x + {cos}^{ - 1} x = \frac{\pi}{2} \\ compare \\ {sin}^{ - 1} 2x = cos {}^{ - 1} x \\ sin {}^{ - 1} x = {sin}^{ - 1} ( \frac{ \sqrt{1 - {x}^{2} } }{x} ) \\ x = \frac{ \sqrt{1 - {x}^{2} } }{x} \\ {x}^{2} = \sqrt{1 - {x}^{2} } \\ {x}^{4} = 1 - {x}^{2} \\ {x}^{4} + {x}^{2} - 1 = 0$
solve this and get x