Question

For the expression below, write an equivalent algebraic expression that involves x only. Assume x is positive.

sec(sin^-1 1/x)

Answer 1

$Given, sec(sin^{-1}\frac{ 1}{x}) \newline Let y=sin^{-1}\frac{ 1}{x}\newline siny=\frac{ 1}{x}\newline And,\newline sec(sin^{-1}\frac{ 1}{x})=secy=\frac{ 1}{cosy}=\frac{ 1}{\sqrt{1-sin^2y}}=\frac{ 1}{\sqrt{1-(\frac{ 1}{x})^2}}=\frac{ x}{\sqrt{x^2-1}}$