Answer: see below
Explanation:
Use the Difference Identity: cos (A - B) = cos A · cos B + sin A · sin B
Given: A + B + C = π
Subtract C: A + B = π - C
Multiply by 4: 4(A + B = π - C)
Distribute: 4A + 4B = 4π - 4C
Apply cosine: cos (4A + 4B) = cos (4π - 4C)
Difference Identity: cos (4A + 4B) = cos (4π)· cos (4C) + sin (4π) ·sin (4C)
Simplify: cos (4A + 4B) = 1 · cos (4C) + 0 ·sin (4C)
→ cos (4A + 4B) = cos (4C) ←