हल कीजिए : `sin^(-1)x+sin^(-1)2x=(pi)/(3)`.

Explanation

`sin^(-1)x+sin^(-1)2x=(pi)/(3)`
`impliessin^(-1)x+sin^(-1)2x=sin^(-1)""(sqrt3)/(2)`
`impliessin^(-1)2x=sin^(1)""(sqrt(3))/(2)-sin^(-1) x`
`=sin^(-1)[(sqrt(3))/(2)sqrt(1-x^(2))-xsqrt(1-((sqrt3)/(2))^(2))]`
`implies2x=sqrt(3)/(2)sqrt(1-x^(2))-(x)/(2)implies(5x)/(2)=sqrt(3)/(2)=sqrt(1-x^(2))`
`implies5x=sqrt3sqrt(1-x^(2))`
`implies25x^(2)=3(1-x^(2))=3-3x^(3)`
`implies28x^(2)=3impliesx^(2)=(3)/(28)`
`impliesx=+-(sqrt3)/(2sqrt7)`
परन्तु `x=-(sqrt3)/(2sqrt7)`
से समीकरण सन्तुष्ट नहीं होती है।
अतः ` x=(sqrt3)/(2sqrt7)`