Cos6x = 1
6x = 2pik
x = 2pik/6 = pik/3, k ∈Z
sin2x = 0
2x = pik
x = pik/2, k ∈ Z
2x²-3x-2/2=x²+x-3/3
x²-4x=0
x*(x-4)=0
x₁=0
x₂=4
1)
2) (x - y)² + (x - y)(x + y)
(x - y)(x - y) + (x - y)(x + y)
x(x - y) - y(x - y) + x(x + y) - y(x + y)
x² - xy - xy + y² + x² + xy - xy - y²
-xy - xy + xy - xy + y² - y² + x² + x²
-2xy + 2x²
1) sin²β - cos²(α - β) + 2cosα·cosβ·cos(α - β) = sin²β + cos(α - β)·(2cosα·cosβ - cos(α - β)) = sin²β + cos(α - β)·(2cosα·cosβ - (cosα·cosβ + sinα·sinβ)) = sin²β + (cosα·cosβ + sinα·sinβ)·(cosα·cosβ - sinα·sinβ) = sin²β + cos²α·cos²β - sin²α·sin²β = sin²β·(1 - sin²α) + cos²α·cos²β = sin²β·cos²α + cos²α·cos²β = cos²α·(sin²β + cos²β) = cos²α
2) cos²β + cos²(α - β) - 2cosα·cosβ·cos(α - β) = cos²β + cos(α - β)·(cos(α - β) - 2cosα·cosβ) = cos²β + cos(α - β)·(cosα·cosβ + sinα·sinβ - 2cosα·cosβ) = cos²β + (cosα·cosβ + sinα·sinβ)·(sinα·sinβ - cosα·cosβ) = cos²β + sin²α·sin²β - cos²α·cos²β = cos²β·(1 - cos²α) + sin²α·sin²β = cos²β·sin²α + sin²α·sin²β = sin²α·(sin²β + cos²β) = sin²α