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`

Options

A. `(7)/(13)`
B. `(4)/(3)`
C. `13`
D. `(13)/(7)`

Answer

C

Explanation

Put `sin^(-1).(5)/(x) = A " or " (5)/(x) = sin A`
`sin^(-1).(12)/(x) = B " or " (12)/(x) = sin B`
`rArr A + B = (pi)/(2)`
`rArr sin A = sin ((pi)/(2) - B) = cos B = sqrt(1 - sin^(2) B)`
`rArr (5)/(x) = sqrt(1 - (144)/(x^(2))) " or " (169)/(x^(2)) = 1`
or `x^(2) = 169 " or " x = 13`
[ `:' x = -13` does not satisfy the given equation]