If `sin^(-1)(5/x)+sin^(-1)((12)/x)=pi/2,` then `x` is equal to `7/(13)` (b) `4/3` (c) `13` (d) `(13)/7`

Explanation

Let `sin^-1(5/x) = A=>sinA = 5/x`

Let `sin^-1(12/x) = B=>sinB = 12/x`

so, the given equation becomes,

`A+B = pi/2`

`=>A = pi/2 - B`

`=>sinA = sin(pi/2-B) = cosB`

`=>sinA = sqrt(1-sin^2B)`

`=>5/x = sqrt(1-(12/x)^2)`

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