Solve `sin^(-1) x + sin^(-1) (1 - x) = cos^(-1) x`

Explanation

We have `sin^(-1) x + sin^(-1) (1 - x) = cos^(-1) x`
`rArr sin^(-1) [x sqrt(1 - (1-x)^(2)) + sqrt(1 - x^(2)) (1 -x)] = sin^(-1) sqrt(1 -x^(2))`
`rArr x sqrt(1-(1 - x)^(2)) + sqrt(1 - x^(2)) (1 - x) = sqrt(1 -x^(2))`
`rArr x sqrt(1-(1 - x)^(2)) = x sqrt(1 - x^(2))`
`rArr x = 0 " or " 2x - x^(2) = 1 - x^(2)`
`rArr x = 0 " or " x = (1)/(2)`