Task/27295435
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Определите число корней уравнения √3 tg2x +3 =0 ,принадлежащих
отрезку [ π/3 ; 3π/2] .
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tg2x = - √3 ;
2x = -π/3 +πn , n∈Z .
x = -π/6 +(π/2)*n , n∈Z .
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π/3 ≤ -π/6 +(π/2)*n ≤ 3π/2 || * 2 / π
2/3 ≤ -1/3 + n ≤ 3 ;
1/3 +1/3 ≤ n ≤ 3 + 1/3 ;
1 ≤ n ≤ 3+1/3 ⇒ n = {1 ; 2 ;3}.
ответ : 3. * * * { π/3 ; 5π/6 ; 4π/3 } * * *