If $\sin^{-1}(\frac{x}{5})+cosec^{-1}(\frac{5}{4})=\frac{π}{2}$ then the value of x is:

3

$∵\sin^{-1}(\frac{x}{5})+cosec^{-1}(\frac{5}{4})=\frac{π}{2}$

$⇒\sin^{-1}(\frac{x}{5})+\sin^{-1}(\frac{4}{5})=\frac{π}{2}⇒\sin^{-1}(\frac{x}{5})=\frac{π}{2}-\sin^{-1}(\frac{4}{5})$

$⇒\sin^{-1}(\frac{x}{5})=\cos^{-1}(\frac{4}{5})⇒\sin^{-1}(\frac{x}{5})=\sin^{-1}(\frac{3}{5})$

$∴x=3$