Question

GPT: \(\sin\left(2x-10^o\right)=-\dfrac{\sqrt{3}}{2}\)

Answer 1

\(\Leftrightarrow\sin\left(2x-10^o\right)=\sin\left(-60^o\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-10^o=-60^o+k360^o\\2x-10^o=180^o-\left(-60^o\right)+k360^o\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=-50^o+k360^o\\2x=250^o+k360^o\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-25^o+k180^o\\x=125^o+k180^o\end{matrix}\right.\left(k\in Z\right)\)