Question

Giải phương trình.

Sin[sin(x+π/3)] =0

Answer 1

\(\Leftrightarrow sin\left(x+\frac{\pi}{3}\right)=k\pi\)

Do \(-1\le sin\left(x+\frac{\pi}{3}\right)\le1\Rightarrow-1\le k\pi\le1\)

\(\Rightarrow-\frac{1}{\pi}\le k\le\frac{1}{\pi}\Rightarrow k=0\)

\(\Rightarrow sin\left(x+\frac{\pi}{3}\right)=0\)

\(\Leftrightarrow x+\frac{\pi}{3}=l\pi\)

\(\Leftrightarrow x=-\frac{\pi}{3}+l\pi\)

Answer 2

Lời giải:

$\sin [\sin (x+\frac{\pi}{3})]=0$

$\Rightarrow \sin (x+\frac{\pi}{3})=k\pi$ với $k\in\mathbb{Z}$

Mà: $\sin (x+\frac{\pi}{3})\in [-1;1]$ nên $k\pi [-1;1]$

Do $k$ nguyên nên $k=0$

$\Rightarrow \sin (x+\frac{\pi}{3})=0$

$\Rightarrow x+\frac{\pi}{3}=m\pi$ với $m$ nguyên

$\Rightarrow x=\pi (m-\frac{1}{3})$ với $m$ nguyên.