If $sin^{-1}(\frac{x}{5})+cosec^{-1}(\frac{5}{4})=\frac{\pi}{2},$ then the value of x is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3
$cosec^{-1}(\frac{5}{4})+\sin^{-1}(\frac{x}{5})=\frac{\pi}{2}$
$\sin^{-1}(\frac{x}{5})=\sec^{-1}\frac{5}{4}$
$\sin^{-1}(\frac{x}{5})=\cos^{-1}\frac{4}{5}$
so $x=3$ as $3^2+4^2=5^2$