solve`:sin^-1x+sin^-1 2x=pi/3`

Explanation

`sin^(-1)x + sin^(-1)2 x = (pi)/(3)`
`rArr " "sin^(1)x + sin^(1)2x = sin ^(1).(sqrt(3))/(2) sin^(-1)2x = sin^(1).sqrt(3)/(2) -sin^(-1)x`
`" "=sin^(1)[(sqrt(3))/(2) sqrt(1-x^(2) )-xsqrt(1-((sqrt(3))/(2))^(2))]`
`rArr" "2x = sqrt(3)/(2)sqrt(1-x^(2))-(x)/(2)`
`rArr" "(5x)/(2) =(sqrt(3))/(2) sqrt(1-x^(2))`
`" "5x = sqrt(3) sqrt(1-x^(2))`
`25x^(2) = 3(1-x^(2))=3-3x^(2)`
`rArr " "28x^(2) =3`
`rArr " "x^(2) =(3)/(28)`
` rArr" "x = pm (sqrt(3))/(2sqrt(7))`
but gives equation is not satisfied by `x= - sqrt(3)/(2sqrt(7))`
Therefore `x=sqrt(3)/(2sqrt(7))`