Đáp án:
1) $C. x = \pm \dfrac{\pi}{3} + k\pi$
2) $B. \dfrac{3\pi}{2}$
Giải thích các bước giải:
1) $\sin^2x + \sin^2x\tan^2x = 3 \qquad (1)$
$ĐK:\, x \ne \dfrac{\pi}{2}+n\pi$
$(1)\Leftrightarrow \sin^2x(\tan^2x + 1) = 3$
$\Leftrightarrow \dfrac{\sin^2x}{\cos^2x} = 3$
$\Leftrightarrow \tan^2x = 3$
$\Leftrightarrow \tan x = \pm \sqrt3$
$\Leftrightarrow x = \pm \dfrac{\pi}{3} + k\pi\quad (k\in\Bbb Z)$
2) $\tan5x - \tan x = 0$
$\Leftrightarrow \tan5x = \tan x$
$\Leftrightarrow 5x = x + k\pi$
$\Leftrightarrow x = k\dfrac{\pi}{4}\quad (k\in\Bbb Z)$
Ta có: $x \in [0;\pi)$
$\Leftrightarrow 0 \leq k\dfrac{\pi}{4}< \pi$
$\Leftrightarrow 0 \leq k < 4$
$\Rightarrow k = \left\{0;1;2;3\right\}$ $(k\in\Bbb Z)$
$\Rightarrow x=\left\{0;\dfrac{\pi}{4};\dfrac{\pi}{2};\dfrac{3\pi}{4}\right\}$
$\Rightarrow \sum x = \dfrac{3\pi}{2}$
