№ 2 Cos² x - 1 - Cos x = √3/2 - Sin² x Cos ²x + Sin ² x - 1 - Cos x = √3/2 - Cos x = √3/2 Cos x = -√3/2 x = 5π/6 №3 2Cos² x - Sin x Cos x + 5sin² x = 3·1 2Cos² x - Sin x Cos x + 5sin² x = 3·(Sin ²x + Cos² x) 2Cos² x - Sin x Cos x + 5sin² x = 3Sin² x + 3Cos² x 2Cos² x - Sin x Cos x + 5sin² x - 3 Sin² x - 3Cos²x = 0 2Sin ²x - Cos² x - Sin xCos x = 0 | :Cos² x≠ 0 2tg² x - tg x -1 = 0 решаем как квадратное a) tg x = 1 б) tg x = -1/2 x = π/4 + πk , k∈Z x = arctg(-1/2) + πn, n ∈Z
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№ 2Cos² x - 1 - Cos x = √3/2 - Sin² x
Cos ²x + Sin ² x - 1 - Cos x = √3/2
- Cos x = √3/2
Cos x = -√3/2
x = 5π/6
№3
2Cos² x - Sin x Cos x + 5sin² x = 3·1
2Cos² x - Sin x Cos x + 5sin² x = 3·(Sin ²x + Cos² x)
2Cos² x - Sin x Cos x + 5sin² x = 3Sin² x + 3Cos² x
2Cos² x - Sin x Cos x + 5sin² x - 3 Sin² x - 3Cos²x = 0
2Sin ²x - Cos² x - Sin xCos x = 0 | :Cos² x≠ 0
2tg² x - tg x -1 = 0
решаем как квадратное
a) tg x = 1 б) tg x = -1/2
x = π/4 + πk , k∈Z x = arctg(-1/2) + πn, n ∈Z