(А*sina+B*cosa)^2+(A*cosa-B*sina)^2

Question

(А*sina+B*cosa)^2+(A*cosa-B*sina)^2

Answer 1

A²sin²a+2ABsinacosa+B²cos²a+A²sin²a-2ABsinacosa+B²cos²a=
=2A²sin²a+2B²cos²a=2(A²-B²)sin²a+2B²=2A²-2(A²-B²)cos²a