Question

Упростите выражения:
1) cos5x cos2x+sin5x sin2x; 2) cos3x cosx-sin3x sinx;
3) cosß sin5ß-sinß cos5B; 4) sin3a cos2a+sin2a cos3a.

Answer 1

Ответ:

cosX * cos3X – sinX * sin3X = cos(X + 3X) = cos4X

sin2X * cosX + cos2X * sinX = sin(2X + X) = sin3X

sinX * cos3X + cosX * sin3X = sin(X + 3X) = sin4X

cosX * cos2X + sinX * sin2X = cos(X + 2X) = cos3X