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
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Answers & Comments
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