(3sin(a)+2cos(a))^2+(2sin(a)-3cos(a))^2

[3 * sin (a) + 2cos (a)] ^ 2 + [2sin (a) - 3 * cos (a)] ^ 2 =

[9 * sin ^ 2 (a) + 2 * 3 * sin (a) * 2 * cos (a) + 4 * cos ^ 2  (a)] +

[4 * sin ^ 2 (a) - 2 * 2 * sin (a) * 3 * cos (a) + 9 * cos ^ 2  (a)] =

9 *[ (sin ^ 2 (a) + cos ^ 2  (a)] + 4 * [sin ^ 2 (a) + cos ^ 2  (a)]  + 2 * 3 *sin (a) * 2cos (a) - 2 * 3sin (a) * 2cos (a) =

9 * [ 1 ] + 4 * [ 1 ] + 12 * sin (a) * cos (a) - 12 * sin (a) * cos (a) = 9 + 4 = 13.