Solve the equation

Question

Solve the equation: arctan x + arccos x = π/4

Answer 1

If an algebraic solution exists, I am not aware of it. Experience says that two angles that have the same tangent and cosine shall not have measures that cleanly add up to π/4. So this must be a mind exercise.

 

I know

tan^-1 1 = π/4.

 

Then I realize that

cos^-1 1 = 0

 

x = 1