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

balajia | Student

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`