Question

пожалуйста помогите решить​

Answer 1

1)cos(x+π/3) = cosx•cosπ/3 - sinx•sinπ/3 = 1/2cosx - ✓3/2sinx

2)sin(x-π/3) = sinx•cosπ/3 - cosx•sinπ/3 = 1/2sinx - ✓3/2cosx

3)sin(x-π/3)•cos(x+π/3) = 1/4cosx•sinx - ✓3/4sin²x - ✓3/4cos²x + 3/4cosx•sinx = cosx•sinx -✓3/4(sin²x+cos²x) = 1/2sin2x - ✓3/4

4) 1/2sin2x - ✓3/4 = -✓3/2

1/2sin2x = -✓3/4

sin2x = -✓3/2

2x = (-1)ⁿ•(-π/3) + πn

x = (-1)^n+1 • π/6 + π/2 n, n€Z