#arctanx# is the angle whose **tangent ratio** is #x#.

#arccos(5/13)# is the angle whose **cosine ratio** is #5/13#.

As we have #arctanx=arccos(5/13)#,

this means the two angles whose tangent ratio is #x# and the other whose cosine ratio is #5/13# are identical.

This means #x# is the tangent of the angle, whose cosine ratio is #5/13#. Let the angle be #A#.

As cosine ratio is #5/13#, we have #cosA=5/13=# and hence using a scientific calculator, we get #A=67.38^@# or #360^@-67.38^@=292.62^@#

i.e. #arctanx=arccos(5/13)=67.38^@# or #292.62^@#

#secA=13/5# and #tanA=sqrt(sec^2A-1)=sqrt((13/5)^2-1)#

= #+-12/5# i.e. #x=+-12/5#

Note that while #tan67.38^@=12/5#, #tan292.62^@=12/5#