Trig
posted by Hannah .
cos[(tan^1(3/4))+(cos^1(9/41))]

let tan^1 (3/4) = A and let cos^1 (9/41) = B
then cos[(tan^1(3/4))+(cos^1(9/41))]
= cos(A + B)
= cosA cosB  sinA sinB
IF tan^1 (3/4) = A
then tanA = 3/4
> sinA = 3/5 and cosA = 4/5, recognize the 345 right angled triangle
if cos^1 (9/41) = B
then cosB = 9/41
> x^2 + y^2 = r^2
81 + y^2 = 1681
y^2 = 1600
y = √1600 = 40 and thus sinB = 40/41
so back to
cosA cosB  sinA sinB
= (4/5)(9/41)  (3/5)(40/41) = 84/205
( I tested my answer with my calculator, it is correct)