If `sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2)` is equal to 1 (b) 2 (c) `1/2` (d) none of these

Explanation

`sin^(-1)x=pi/2-sin^(-1)y`

`sin^(-1)x=cos^(-1)y`

`sin^(-1)x=sin^(-1)sqrt(1-y^2)`

`x=sqrt(1-y^2`

`x^2=1-y^2`

`x^2+y^2=1-(1)`

`(1+x^4+y^4)/((x^2-x^2y^2)+y^2)=(1+(x^2+y^2)^2-2x^2y^2)/(1-x^2y^2)`

`(1+(x^2+y^2)^2-2x^2y^2)/(1-x^2y^2)`

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