Solve the following equation: `sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x`

1.	Solve the following equation: `sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x`
Answer» `sin^(-1) x + sin^(-1) (1-x) = cos^(-1)x ` `rArr " "sin[xsqrt(1-(1-x)^(2)) +(1-x)sqrt(1-x^(2))]= sin ^(-1)sqrt(1-x^(2))` `rArr xsqrt(2x-x^(2)) + sqrt(1-x)- xsqrt(1-x^(2)) = sqrt(1-x^(2))` `rArr " "xsqrt(2x-x^(2)) + xsqrt(1-x^(2)) = 0` `rArr" "x[sqrt(2x-x^(2)) -sqrt(1-x^(2))]=0` `rArr x = 0 or sqrt(2x-x^(2))-sqrt(1-x^(2))=0` Now `sqrt(2x-x^(2))-sqrt(1-x^(2)) = 0` `rArr" "sqrt(2x -x^(2)) = sqrt(1-x^(2))` `rArr" "2x -x^(2) = 1- x^(2)` `rArr " "2x =1` `rArr " " x=1//2` ` therefore " "x=0 or x = 1//2`

Discussion

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