решите тригонометрическое уравнение
[tex] 4tg^2 + \frac{3}{sin( \frac{3 \pi }{2)})+x}+3 =0[/tex]
[tex] 4tg^2 + \frac{3}{sin( \frac{3 \pi }{2)})+x}+3 =0[/tex]
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В знаменателе применим формулу приведения:4tg²x - 3/cosx + 3 = 0
Умножим на cos²x:
4sin²x - 3cosx + 3cos²x = 0
4(1 - cos²x) - 3cosx + 3cos²x = 0
cos²x + 3cosx - 4 = 0
cosx = t
t² + 3t - 4 = 0
D = 9 + 16 = 25
t = 1 t = - 4
cosx = 1 cosx = - 4
x = 2πn нет корней