Question

помогите решить уравнение
√3tgx + 3 = 3/cos²x

Answer 1

Ответ:

решение на фотографии

Answer 2

$\sqrt{3}tgx+3=\frac{3}{Cos^{2}x} \\\\\sqrt{3}tgx+3=3(1+tg^{2}x)\\\\\sqrt{3}tgx+3=3+3tg^{2}x\\\\3tg^{2}x-\sqrt{3}tgx=0\\\\\sqrt{3}tg^{2}x-tgx=0\\\\tgx(\sqrt{3}tgx-1)=0\\\\\left[\begin{array}{ccc}tgx=0\\\sqrt{3}tgx-1=0 \end{array}\right\\\\\\\left[\begin{array}{ccc}tgx=0\\tgx=\frac{1}{\sqrt{3}} \end{array}\right\\\\\\\left[\begin{array}{ccc}x=\pi n,n\in Z \\x=\frac{\pi }{6}+\pi n,n\in z \end{array}\right$