tan3x tanx = 1 mn giai giup cam on nhieu 30/09/2021 Bởi Caroline tan3x tanx = 1 mn giai giup cam on nhieu
$$\eqalign{ & \tan 3x.\tan x = 1\,\,\left( {DK:\,\,\cos 3x \ne 0;\,\,\cos x \ne 0} \right) \cr & \Leftrightarrow \tan 3x = {1 \over {\tan x}} \cr & \Leftrightarrow \tan 3x = \cot x = \tan \left( {{\pi \over 2} – x} \right) \cr & \Leftrightarrow 3x = {\pi \over 2} – x + k\pi \cr & \Leftrightarrow 4x = {\pi \over 2} + k\pi \Leftrightarrow x = {\pi \over 8} + {{k\pi } \over 4}\,\,\left( {k \in Z} \right)\,\,\left( {tm} \right) \cr} $$ Bình luận
Đáp án: x=pi/8+kpi/4; k thuộc Z
Giải thích các bước giải:
$$\eqalign{
& \tan 3x.\tan x = 1\,\,\left( {DK:\,\,\cos 3x \ne 0;\,\,\cos x \ne 0} \right) \cr
& \Leftrightarrow \tan 3x = {1 \over {\tan x}} \cr
& \Leftrightarrow \tan 3x = \cot x = \tan \left( {{\pi \over 2} – x} \right) \cr
& \Leftrightarrow 3x = {\pi \over 2} – x + k\pi \cr
& \Leftrightarrow 4x = {\pi \over 2} + k\pi \Leftrightarrow x = {\pi \over 8} + {{k\pi } \over 4}\,\,\left( {k \in Z} \right)\,\,\left( {tm} \right) \cr} $$