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Find x if sin^-1(5/x) + sin^-1(12/x) =pi/2

\sin^{- 1} (\frac{5}{x}) + \sin^{- 1} (\frac{12}{x}) = \frac{π}{2} A s w e k n o w t h a t, \sin^{- 1} x + \cos^{- 1} x = \frac{π}{2} s o, \sin^{- 1} (\frac{5}{x}) = \frac{π}{2} - \sin^{- 1} (\frac{12}{x}) = \cos^{- 1} (\frac{12}{x}) N o w w e k n o w t h a t \cos^{- 1} x = \sin^{- 1} \sqrt{1 - x^{2}} S o \sin^{- 1} (\frac{5}{x}) = \sin^{- 1} \sqrt{1 - {(\frac{12}{x})}^{2}} o r (\frac{5}{x}) = \sqrt{1 - {(\frac{12}{x})}^{2}} o r \frac{25}{x^{2}} = 1 - \frac{144}{x^{2}} \frac{169}{x^{2}} = 1 o r x = \pm 13

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