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

Sagot :

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]

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