`cot(arctan(1/x))` Write an algebraic expression that is equivalent to the given expression. (Hint: Sketch a right triangle.)

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balajia | College Teacher | (Level 1) eNoter

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

`tan^-1(1/x)=cot^-1(x/1)=cot^-1x`

`cot(tan^-1(1/x))=cot(cot^-1x)=x`