`sec(arcsin(x - 1))` Write an algebraic expression that is equivalent to the given expression. (Hint: Sketch a right triangle.)

Textbook Question

Chapter 4, 4.7 - Problem 70 - Precalculus (3rd Edition, Ron Larson).
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balajia | College Teacher | (Level 1) eNoter

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Taking (x-1) as oppsite side and 1 as the hypotenuse,the adjacent side  will be equal to `sqrt(1-(x-1)^2)=sqrt(2x-x^2)`

`sin^-1(x-1)=sec^-1(1/(sqrt(2x-x^2)))`

`sec(sin^-1(x-1))=sec(sec^-1(1/(sqrt(2x-x^2))))`

`=1/(sqrt(2x-x^2))`

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