Відповіді АЛГЕБРА: 16.25 (1-2)

16.25

1) sin4xcos4x = 34/ x2;

2sin4xcos4x = 34

sin8x = 34

8x = (–1)ⁿ π3 + πn, n є z;

x = (–1)ⁿ π24 + 18 πn, n є z.

2) sin²(x + π3) – cos²(x + π3) = 1;

–cos(2x + 2π3) = 1;

cos(2x + 2π3) = –1;

2x + 2π3 = π + 2πn, n є z;

2x + π3 + 2πn, n є z;

x = π6 + πn, n є z.

3) sin4x cosx – cos4x sinx = 12

sin3x = 12

3x = (–1)ⁿ π6 + πn, n є z;

x = (–1)ⁿ π18 + 13 πn, n є z;

4) sin²x3 = 34

1-cos2x32 = 34

1 – cos2x3 = 32

cos2x3 = –12

2x3 = ± (π – π3) + 2πn, n є z;

2x3 = ± 2π3 + 2πn;

2x = ± 2π + 6πn;

x = ± π + 3πn, n є z.