Answer:
see explanation
Step-by-step explanation:
Consider the left side
(Acosx + Bsinx)² - (Bcosx + Asinx)² ← expand factors using FOIL
= A²cos²x + 2ABsinxcosx + B²sin²x - (B²cos²x + 2ABsinxcosx + A²sin²x)
= A²cos²x + 2ABsinxcosx + B²sin²x - B²cos²x - 2ABsinxcosx - A²sin²x
= A²cos²x - Bcos²x + B²sin²x - A²sin²x ← factor first/second and third/fourth terms
= cos²x(A² - B²) - sin²x(A² - B²) ← factor out (A² - B²) from each term
= (A² - B²)(cos²x - sin²x)
= right side ⇒ proven
