1) 1=1²=(sin²x+cos²x)²=sin⁴x+cos⁴x+2sin²xcos²x=sin⁴x+cos⁴x+2(sinxcosx)²,
sinxcosx=1/2sin2x=1/2 *2/5=1/5
sin⁴x+cos⁴x= 1-2(sinxcosx)²=1-2 * 1/25=23/25
(sin⁴x+cos⁴x)²=sin⁸x+cos⁸x+2sin⁴xcos⁴x=sin⁸x+cos⁸x+2(sinxcosx)⁴=sin⁸x+cos⁸x+2(1/5)⁴
sin⁸x+cos⁸x=(23/25)²-2(1/5)⁴= 529/625 -2/625= 527/625
2) (cos15-sin15)²=a²/ (16cos²15)
cos²15+sin²15-2sin15cos15=1-sin30=1-1/2=1/2
1/2=a²/(16cos²15) ⇒ a²=8cos²15= 8 *(1+cos30)/2=4(1+√3/2)= 2(2+√3), a=2√(2+√3)
Формула: cos²x=(1+cos2x)/2
sin2x=2sinxcosx
sin²x+cos²x=1
У=x^2-6х-7
D=36+28=64, х₁=14, х₂=-2
<span>А) |2х| = 3.
2х = 3, х = 3/2.
и 2х = -3, х = -3/2.
Б) |х+2| =7.
х + 2 = 7, х = 7 - 2 = 5,
х + 2 = -7 = -7 - 2 = -9.
В) |5х-8| = 0.
5х - 8 = 0.
х = 8/5.</span>
A^2 + 6a + 9 + a^2 - 9 + 6a =
= 2a^2 + 12a =
= 2a (a + 6)