Answer to Question #185677 in Trigonometry for Tim

Question #185677

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


sec(sin^-1 1/x)


1
Expert's answer
2021-05-10T17:12:45-0400

Given,sec(sin11x)Lety=sin11xsiny=1xAnd,sec(sin11x)=secy=1cosy=11sin2y=11(1x)2=xx21Given, 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}}


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