Question

Find the value of `tan(cos^(-1)(3/x))`?

Answer 1

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

Explanation:

Let `cos^(-1)(3/x)=t`

then `cost=3/x`

and therefore `sect=x/3`

and `sec^2x=x^2/9` and `tan^2t=x^2/9-1=(x^2-9)/9`

and `tant=1/3sqrt(x^2-9)`

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