Final answer:
To expand cos(75) using sum/difference formulas, we can use the expression cos(45 + 30), which simplifies to (sqrt(6)/4) - (sqrt(2)/4).
Step-by-step explanation:
The cosine function can be expanded using the sum/difference formulas. For cos(75), we can use the sum formula to express it as cos(45 + 30). Applying the formula, we get cos(75) = cos(45)cos(30) - sin(45)sin(30).
cos(45) = sqrt(2)/2 and cos(30) = sqrt(3)/2, while sin(45) = sqrt(2)/2 and sin(30) = 1/2.
Substituting the values, we have cos(75) = (sqrt(2)/2)(sqrt(3)/2) - (sqrt(2)/2)(1/2).
Simplifying the expression, we get cos(75) = (sqrt(6)/4) - (sqrt(2)/4).