Question

Evaluate sec(cos^-1(tan(sin^-1(a/b)))) where a/b is a positive real number

Answer 1

Simplify the expression.

`\begin{gathered} \sec (\cos ^(-1)(\tan (\sin ^(-1)((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}`

So answer is

`\frac{\sqrt[]{a^2+b^2}}{a}`