Cos (x+pi/3)+cos (x-pi/3)=10 Giup e vs nha 01/07/2021 Bởi Julia Cos (x+pi/3)+cos (x-pi/3)=10 Giup e vs nha
Đáp án: $x = k\pi\quad (k\in\Bbb Z)$ Giải thích các bước giải: $\cos\left(x + \dfrac{\pi}{3}\right) + \cos\left(x – \dfrac{\pi}{3}\right) = \dfrac{1}{\cos x}\qquad (*)$ $ĐKXĐ:\, x \ne \dfrac{\pi}{2} + n\pi$ $(*)\Leftrightarrow 2\cos\left(\dfrac{x + \dfrac{\pi}{3} + x – \dfrac{\pi}{3}}{2}\right).\cos\left(\dfrac{x + \dfrac{\pi}{3} – x +\dfrac{\pi}{3}}{2}\right)=\dfrac{1}{\cos x}$ $\Leftrightarrow \cos x\cos\dfrac{\pi}{3} = \dfrac{1}{2\cos x}$ $\Leftrightarrow \cos^2x.\dfrac{1}{2} = \dfrac{1}{2}$ $\Leftrightarrow \cos^2x = 1$ $\Leftrightarrow \cos x = \pm 1$ $\Leftrightarrow x = k\pi\quad (k\in\Bbb Z)$ Bình luận
Đáp án:
$x = k\pi\quad (k\in\Bbb Z)$
Giải thích các bước giải:
$\cos\left(x + \dfrac{\pi}{3}\right) + \cos\left(x – \dfrac{\pi}{3}\right) = \dfrac{1}{\cos x}\qquad (*)$
$ĐKXĐ:\, x \ne \dfrac{\pi}{2} + n\pi$
$(*)\Leftrightarrow 2\cos\left(\dfrac{x + \dfrac{\pi}{3} + x – \dfrac{\pi}{3}}{2}\right).\cos\left(\dfrac{x + \dfrac{\pi}{3} – x +\dfrac{\pi}{3}}{2}\right)=\dfrac{1}{\cos x}$
$\Leftrightarrow \cos x\cos\dfrac{\pi}{3} = \dfrac{1}{2\cos x}$
$\Leftrightarrow \cos^2x.\dfrac{1}{2} = \dfrac{1}{2}$
$\Leftrightarrow \cos^2x = 1$
$\Leftrightarrow \cos x = \pm 1$
$\Leftrightarrow x = k\pi\quad (k\in\Bbb Z)$