Question

Помогите промежуток [5pi/2; 4pi]

Answer 1

$\frac{3tg^2x}{\sqrt{7cosx}} =0\; ,\; \; ODZ:\; \; cosx \ \textgreater \ 0\; \to \; -\frac{\pi}{2}+\pi n\ \textless \ x\ \textless \ \frac{\pi}{2}+\pi n,\; n\in Z\\\\tg^2x=0\; ,tgx=0\; \to \; x=\pi k\; ,\; k\in Z\\\\ \left \{ {{x=\pi k} \atop {-\frac{\pi}{2}+\pi n\ \textless \ x\ \textless \ \frac{\pi}{2}+\pi n}} \right. \; \Rightarrow \; \; x=2\pi k,\; k\in Z\\\\x\in [\; \frac{5\pi }{2};4\pi \, ]\; \; \Rightarrow \; \; x=4\pi \; .$