Решите уравнения:

1. sin^ (2) 7x - cos^ (2) 7x = корень из 3 делить на 2.

2. cosx/4 * sinП/5 - sinx/4 * cosП/5 = корень из 3 делить на 2.

1. sin² 7x - cos² 7x = √3/2

- (cos² 7x - sin² 7x) = √3/2

- cos (2*7x) = √3/2

- cos 14x = √3/2

cos 14x = - √3/2

14x = + 5π/6 + 2πk, k∈Z

x = + 5π/84 + πk/7, k∈Z

2. cosx/4 * sin π/5 - sinx/4 cos π/5 = √3/2

sin π/5 * cosx/4 - cos π/5 * sinx/4 = √3/2

sin (π/5 - x/4) = √3/2

1) π/5 - x/4 = π/3 + 2πn, n∈Z

-x/4 = π/3 - π/5 + 2πn

-x/4 = 2π/15 + 2πn

x = - 8π/15 - 8πn, n∈Z

2) π/5 - x/4 = π - π/3 + 2πn, n∈Z

π/5 - x/4 = 2π/3 + 2πn

-x/4 = 2π/3 - π/5 + 2πn

-x/4 = 7π/15 + 2πn

x = - 28π/15 - 8πn, n∈Z

Ответ: - 8π/15 - 8πn, n∈Z;

-28π/15 - 8πn, n∈Z.