Question

sin(4x-10°) = √2/2

Answer 1

\(\sin\left(4x-10^0\right)=\dfrac{\sqrt{2}}{2}\\ \Leftrightarrow4x-10^0=45^0\\ \Leftrightarrow4x=55^0\Leftrightarrow x=13,75^0\)

Answer 2

\(\Leftrightarrow sin\left(4x-10^0\right)=sin\left(45^0\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}4x-10^0=45^0+k360^0\\4x-10^0=135^0+k360^0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}4x=55^0+k360^0\\4x=145^0+k360^0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=13,75^0+k90^0\\x=36,25^0+k90^0\end{matrix}\right.\) (\(k\in Z\))