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danilarogalyov
@danilarogalyov
July 2022
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корень из 3 sinx+cosx=1. Помогите из
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yugolovin
Verified answer
Разделим уравнение на 2 и заменим √3/2 на cos π/6, а 1/2 на sin π/6.
sin x·cos π/6+cos x·sin π/6=1/2;
sin(x+π/6)=1/2;
x+π/6= π/6+2πn или x+π/6=5π/6+2πk.
Ответ: x=2πn или x=2π/3+2πk; n, k∈Z
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Answers & Comments
Verified answer
Разделим уравнение на 2 и заменим √3/2 на cos π/6, а 1/2 на sin π/6.sin x·cos π/6+cos x·sin π/6=1/2;
sin(x+π/6)=1/2;
x+π/6= π/6+2πn или x+π/6=5π/6+2πk.
Ответ: x=2πn или x=2π/3+2πk; n, k∈Z