`tan(arccos(x/3))` Write an algebraic expression that is equivalent to the given expression. (Hint: Sketch a right triangle.)

balajia | Student

Taking x as adjacent side and 3 as the hypotenuse,adjacent side will be equal to

`sqrt(3^2-x^2)=sqrt(9-x^2)`

`cos^-1(x/3)=tan^-1(sqrt(9-x^2)/x)`

`tan(cos^-1(x/3))=tan(tan^-1(sqrt(9-x^2)/x))`

`=sqrt(9-x^2)/x`