Question

How do you solve `\tan ^ { - 1} ( \frac { 12} { 5} ) = \cos ^ { - 1} x`?

Answer 1

`x=5/13`

Explanation:

Set `arctan(12/5)=arccosx=u`, hence `tanu=12/5` and `cosu=x`

After using `cosu=1/sqrt((tanu)^2+1)` identity,

`cosu=x=1/sqrt((12/5)^2+1)=5/13`