Answer :
Simplify the expression.
[tex]\begin{gathered} \sec (\cos ^{-1}(\tan (\sin ^{-1}(\frac{a}{b}))))=\sec (\cos ^{-1}(\tan (\tan ^{-1}\frac{a}{\sqrt[]{a^2+b^2}}))) \\ =\sec (\cos ^{-1}\frac{a}{\sqrt[]{a^2+b^2}}) \\ =\sec (\sec ^{-1}(\frac{\sqrt[]{a^2+b^2}}{a})) \\ =\frac{\sqrt[]{a^2+b^2}}{a} \end{gathered}[/tex]So answer is
[tex]\frac{\sqrt[]{a^2+b^2}}{a}[/tex]