Giải phương trình : sinx= căn 2/2 sinx= -căn3/2

Đáp án:

 $a){\left[\begin{aligned}x=\dfrac{\pi}{4}+k2\pi\\x=\dfrac{3\pi}{4}+k2\pi\end{aligned}\right.},(k\in \mathbb{Z})\\ 
b)
{\left[\begin{aligned}x=\dfrac{-\pi}{3}+k2\pi\\x=\dfrac{4\pi}{3}+k2\pi\end{aligned}\right.},(k\in \mathbb{Z})\\$

Giải thích các bước giải:

 $a) \sin x=\dfrac{\sqrt{2}}{2}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{\pi}{4}+k2\pi\\x=\pi-\dfrac{\pi}{4}+k2\pi\end{aligned}\right.}\\ 
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{\pi}{4}+k2\pi\\x=\dfrac{3\pi}{4}+k2\pi\end{aligned}\right.},(k\in \mathbb{Z})\\ 
b)
\sin x=\dfrac{-\sqrt{3}}{2}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{-\pi}{3}+k2\pi\\x=\pi+\dfrac{\pi}{3}+k2\pi\end{aligned}\right.}\\ 
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{-\pi}{3}+k2\pi\\x=\dfrac{4\pi}{3}+k2\pi\end{aligned}\right.},(k\in \mathbb{Z})\\$