Given sin -1 $\left( {{x \over 5}} \right)$ + cosec -1 $\left( {{5 \over 4}} \right)$ = ${\pi \over 2}$ $\Rightarrow$ sin -1 $\left( {{x \over 5}} \right)$ + sin -1 $\left( {{4 \over 5}} \right)$ = ${\pi \over 2}$ $\Rightarrow$ sin -1 $\left( {{x \over 5}} \right)$ = ${\pi \over 2}$ - sin -1 $\left( {{4 \over 5}} \right)$ $\Rightarrow$ sin -1 $\left( {{x \over 5}} \right)$ = cos -1 $\left( {{4 \over 5}} \right)$ $\Rightarrow$ ${x \over 5}$ = sin(cos -1 ${{4 \over 5}}$) $\Rightarrow$ ${x \over 5}$ = sin(sin -1 ${{3 \over 5}}$) $\Rightarrow$ ${x \over 5}$ = ${3 \over 5}$ $\Rightarrow$ x = 3