समीकरण `sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x` को हल कीजिए।

Explanation

`sin^(-1)x+sin^(-1)(1+x)=cos^(-1)x`
`impliessin^(-1)[xsqrt(1-(1-x)^(2))+(1-x)sqrt(1-x^(2))]=sin^(-1)sqrt(1-x^(2))`
`impliesxsqrt(2x-x^(2))+sqrt(1-x^(2))-xsqrt(1-x^(2))=sqrt(1-x^(2))`
`impliesxsqrt(2x-x^(2))-xsqrt(1-x^(2))=sqrt(1-x^(2))=0`
`impliesx(sqrt(2x-x^(2))-sqrt(1-x^(2)))=0`
`impliesx=0" या "sqrt(2x-x^(2))-sqrt(1-x^(2))=0`
अब `sqrt(2x-x^(2))-sqrt(1-x^(2))=0`
`impliessqrt(2x-x^(2))-sqrt(1-x^(2))implies2x-x^(2)=1-x^(2)`
`implies2x=1" "impliesx=1//2`
`:.x=0" या "x=1//2`