Sin(X-pi/3)=1/2 giúp tớ với

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Đáp án:

\(\left[ \begin{array}{l} x=\dfrac\pi2+k2\pi \\ x=\dfrac{7\pi}6+k2\pi\end{array} \right.,\ (k \in \mathbb{Z})\)

Giải thích các bước giải:

`+)\ sinu=sinv`

\(\Leftrightarrow\left[ \begin{array}{l}u=v+k2\pi\\ u=\pi-v+k2\pi\end{array} \right.,\ (k \in \mathbb{Z})\)

`@)\ sin(x-pi/3)=1/2`

`<=>sin(x-pi/3)=sin(pi/6)`

\(\Leftrightarrow\left[ \begin{array}{l} x-\dfrac\pi3=\dfrac\pi6+k2\pi \\ x-\dfrac\pi3=\pi-\dfrac\pi6+k2\pi\end{array} \right.,\ (k \in \mathbb{Z})\)

\(\Leftrightarrow\left[ \begin{array}{l} x=\dfrac\pi2+k2\pi \\ x=\dfrac{7\pi}6+k2\pi\end{array} \right.,\ (k \in \mathbb{Z})\)

`S={pi/2+k2pi;\ (7pi)/2+k2pi,\ \ k in ZZ}`