`csc(arctan(x/sqrt(2)))` Write an algebraic expression that is equivalent to the given expression. (Hint: Sketch a right triangle.)

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Chapter 4, 4.7 - Problem 73 - Precalculus (3rd Edition, Ron Larson).
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balajia | College Teacher | (Level 1) eNoter

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

`tan^-1(x/sqrt(2))=csc^-1(sqrt(x^2+2)/x)`

`csc(tan^-1(x/sqrt(2)))=csc(csc^-1(sqrt(x^2+2)/x))`

`=sqrt(x^2+2)/x`

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