Câu 1. (1 điểm) Giải các phương trình sau: a) $\sin \left(x+\frac{\pi}{3}\right)=\frac{1}{2}$ b) $\tan \left(x-\frac{3 \pi}{4}\right)=1$

`a. sin(x+pi/3)=1/2`

`<=>sin(x+pi/3)=` $\rm{\sin\dfrac{\pi}{6}}$

`<=>` $\left[\begin{matrix} x+\dfrac{\pi}{3}=\dfrac{\pi}{6}+k2\pi\\x+\dfrac{\pi}{3}=\pi-\dfrac{\pi}{6}+k2\pi \end{matrix}\right.$

`<=>` $\left[\begin{matrix} x+\dfrac{\pi}{3}=\dfrac{\pi}{6}+k2\pi\\x+\dfrac{\pi}{3}=\dfrac{5\pi}{6}+k2\pi \end{matrix}\right.$

`<=>` $\left[\begin{matrix} x=\dfrac{\pi}{6}-\dfrac{\pi}{3}+k2\pi\\x=\dfrac{5\pi}{6}-\dfrac{\pi}{3}+k2\pi \end{matrix}\right.$

`<=>` $\left[\begin{matrix} x=-\dfrac{\pi}{6}+k2\pi\\x=\dfrac{\pi}{2}+k2\pi \end{matrix}\right.$ `(k \in ZZ)`

$\\$

`b. tan(x-(3pi)/4)=1`

`<=>tan(x-(3pi)/4)=` $\rm{\dfrac{\pi}{4}}$

`<=>x-(3pi)/4=pi/4+kpi`

`<=>x=pi/4+(3pi)/4+kpi`

`<=>x=pi+kpi(k \in ZZ)`