Solve `sin^(-1) x cos^(-1) x = sin^(-1) (3x -2)`

1.	Solve `sin^(-1) x cos^(-1) x = sin^(-1) (3x -2)`
Answer» `sin^(-1) x - cos^(-1) x = sin^(-1) (3x -2)` This equation is valid if `-1 le x le 1 and -1 le 3x - 2 le 1` `rArr x in [(1)/(3), 1]` given equation can be rewritten as: `(pi)/(2) - cos^(-1) x = cos^(-1) x = (pi)/(2) - cos^(-1) (3x -2)` `rArr 2 cos^(-1) x = cos^(-1) (3 x -2)` `rArr cos^(-1) (2x^(2) - 1) = cos^(-1) (3x -2)` `rArr 2x^(2) -1 = 3x - 2` `rArr 2x^(2) - 3x + 1 = 0` `rArr x = 1 " or " (1)/(2)`

Discussion

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