To solve the first equation:
ctg(x) = -49/4tan(x) = -4/49x = atan(-4/49) + n pi, where n is an integerx ≈ -0.0808 + n pi
To solve the second equation:
2cos(3x - π/6) - √2 = 0cos(3x - π/6) = √2/23x - π/6 = ±π/4 + 2nπ, where n is an integer3x = π/4 + π/6 ± 2nπ or 3x = 7π/4 + π/6 ± 2nπx = (π/4 + π/6 ± 2nπ) / 3 or x = (7π/4 + π/6 ± 2nπ) / 3
Simplify further by substituting n = 0, 1, 2, etc., to find the exact values of x.
To solve the first equation:
ctg(x) = -49/4
tan(x) = -4/49
x = atan(-4/49) + n pi, where n is an integer
x ≈ -0.0808 + n pi
To solve the second equation:
2cos(3x - π/6) - √2 = 0
cos(3x - π/6) = √2/2
3x - π/6 = ±π/4 + 2nπ, where n is an integer
3x = π/4 + π/6 ± 2nπ or 3x = 7π/4 + π/6 ± 2nπ
x = (π/4 + π/6 ± 2nπ) / 3 or x = (7π/4 + π/6 ± 2nπ) / 3
Simplify further by substituting n = 0, 1, 2, etc., to find the exact values of x.