For the expression below, write an equivalent algebraic expression that involves x only. Assume x is positive.
sec(sin^-1 1/x)
Given,sec(sin−11x)Lety=sin−11xsiny=1xAnd,sec(sin−11x)=secy=1cosy=11−sin2y=11−(1x)2=xx2−1Given, 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}}Given,sec(sin−1x1)Lety=sin−1x1siny=x1And,sec(sin−1x1)=secy=cosy1=1−sin2y1=1−(x1)21=x2−1x
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