Question

Решите уравнение (40б) :$sin(frac{pi}{3} +alpha) - frac{sqrt{3}}{2}cosalpha=0$

Answer 1

sin(α + β) = sinα · cosβ + cosα · sinβ

sin(π/3 + α) - √3/2cosαα α = 0,
sinπ/3 · cosα + cosπ/3 · sinα - √3/2cosαα α = 0,
√3/2cosαα α + cosπ/3 · sinα - √3/2cosαα α = 0,
cosπ/3 · sinα = 0,
1/2 · sinα = 0,
sinα = 0,
α = πn, n ∈ Z