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

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

Discussion

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