Đáp án:
Giải thích các bước giải:
a) `2 cos x-1=0`
`⇔ cos x=1/2`
`⇔ cos x=cos \frac{\pi}{3}`
`⇔ x=±\frac{\pi}{3}+k2\pi\ (k \in \mathbb{Z})`
Vậy ...
b) `tan^2 x-(\sqrt{3}+1)tan x+\sqrt{3}=0`
`⇔` \(\left[ \begin{array}{l}tan x=\sqrt{3}\\tan x=1\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=\dfrac{\pi}{3}+k\pi\ (k \in \mathbb{Z})\\x=\dfrac{\pi}{4}+k\pi\ (k \in \mathbb{Z})\end{array} \right.\)
Vậy .....
c) `sin x+\sqrt{3} cos x=2`
`⇔ \frac{1}{2}sin x+\frac{\sqrt{3}}{2} cos x=1`
`⇔ sin (x+\frac{\pi}{3})=1`
`⇔ x+\frac{\pi}{3}=\frac{\pi}{2}+k2\pi\ (k \in \mathbb{Z})`
`⇔ x=\frac{\pi}{6}+k2\pi\ (k \in \mathbb{Z})`
Vậy ........
