§ 25: 25.32 (1-3)

25.32 Спростіть вираз:

1) cos2αsin22α • (cos2αsin2α - sin2αcos2α) = cos2αsin22α1 • cos4α- sin2αsin2α cos2α = cos2α1 : 4sin2αcos2α • (cos2α - sin2α)(cos2α + sin2α)sin2α cos2α = cos2α1 • 14cos2α = 14;

2) sin2α - 4sin2α2sin2α - 4 + 4sin2α2 = 4sin2α2 cos2α2 - 4sin2 α24sin2 α2 cos2α2 - 4(1 - sin2 α2) = 4sin2 α2(cos2 α2 - 1)4cos2 α2(sin2 α 2 - 1) = sin2α2 • (-sin2 α2)cos2α2 • (-cos2 α2) = sin4α2cos4α2 = tg⁴α2;

3) 2sinπ4 -αcos(π2 - π4 +α)2sin(3α- α)⁡⁡ = 2sin(π4 - α)cos(π4 - α)2 sin 2α⁡= sin(π2 -2α)2sin 2α⁡= cos2α2sin2α = 12ctg2α.

4) tg5π4 - 4α • sin2(5π4 + 4α)1 - 2 cos24α = 1- cos(5π2 - 8α)1+ cos(5π2 - 8α)⁡⁡ • (1- cos(5π2 + 8α)2) : (–cos8α) = 12 1- sin8α1+ sin8α⁡⁡ • (1 + sin8α) : (–cos8α) = 12 (1- sin8α)(1+sin8α)1- sin8α⁡⁡: (–cos8α) = 12 (1- sin8α)(1+ sin8α) : (–cos8α) = 12cos8α : (–cos8α) = –12.