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christinadezhn
@christinadezhn
August 2022
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√3 sinx-cosx=1
Решите, пожалуйста, уравнение. Преобразование тригонометрических выражений, 10 класс.
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gamehacker99
Verified answer
Разделяем на два
√3/2sinx-1/2cosx=1/2
sinx*cos(π/6)-sin(π/6)cosx=1/2
sin(x-π/6)=1/2
x-π/6=(-1)^k*π/6+πk,k∈Z
x=(-1)^k*π/3+πk,k∈Z
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christinadezhn
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Answers & Comments
Verified answer
Разделяем на два√3/2sinx-1/2cosx=1/2
sinx*cos(π/6)-sin(π/6)cosx=1/2
sin(x-π/6)=1/2
x-π/6=(-1)^k*π/6+πk,k∈Z
x=(-1)^k*π/3+πk,k∈Z