Відповіді АЛГЕБРА: 16.26 (1-2)

16.26

1) 4sin x4 cosx4 = 1;

2sin x2 = 1;

sinx2 = 12

x2 = (–1)ⁿ π6 + πn, n є z;

x = (–1)ⁿ π3 + 2πn, n є z;

2) 2cos²(x – π8) – 2sin²(x – π8) = 2;

cos(2x – π4) = 1;

2x – π4 = 2πn, n є z;

2x = π4 + 2πn, n є z;

x = π8 + πn, n є z.

3) sin5x cos3x + cos5x sin3x = –22

sin8x = –22

8x = (–1)ⁿ⁺¹–π4 + πn, n є z;

x = (–1)ⁿ⁺¹ π32 + 18πn, n є z;

4) cos² 3x2 = 12

1+cos3x2 = 12

cos3x = 0

3x = π2 + πn, n є z;

x = π6 + 13πn, n є z;

x² = 2πn, n є z;

x = ± 2πn, n є z.