Final answer:
The expression 'cos(pi/4) cos(pi/9) - sin(pi/4) sin(pi/9)' can be simplified using the cosine sum formula, resulting in 'cos(pi/4 + pi/9)'.
Step-by-step explanation:
The student's question involves finding the expression for the cosine of an angle, using the sum and difference formulas for cosine. The original expression is cos(pi/4) cos(pi/9) - sin(pi/4) sin(pi/9). According to the sum and difference identities for cosine, cos(A)cos(B) - sin(A)sin(B) is equal to cos(A + B). Therefore, the given expression simplifies to cos(pi/4 + pi/9), which is the cosine of the sum of the two angles.