"Write cos(arctan 1 + arccos x) as an algebraic expression." So, I understand that I am to use formula for cos(u + v) because it fits the expression, where u = arctan 1 and
v = arccos x. I also know that I must create to right triangles for each of the angles u and v, the reason being that the angles are likely to be different. What I do not understand is why, when the formula is used, we don't evaluate cos(arctan 1) as
cos(pi/4), which then equals 0. In the book, cos(arctan 1) is evaluated as
1/sqroot(2). Perhaps I do not understand inverse trigonometric functions as I thought I did.