a.
\(sin5x=-\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}5x=-\dfrac{\pi}{4}+k2\pi\\5x=\dfrac{5\pi}{4}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{20}+\dfrac{k2\pi}{5}\\x=\dfrac{\pi}{4}+\dfrac{k2\pi}{5}\end{matrix}\right.\)
b.
\(tan\left(2x+\dfrac{\pi}{4}\right)=-1\)
\(\Leftrightarrow2x+\dfrac{\pi}{4}=-\dfrac{\pi}{4}+k\pi\)
\(\Leftrightarrow x=-\dfrac{\pi}{4}+\dfrac{k\pi}{2}\)
c.
\(cos3x=-\dfrac{\sqrt{3}}{2}\)
\(\Leftrightarrow3x=\pm\dfrac{5\pi}{6}+k2\pi\)
\(\Leftrightarrow x=\pm\dfrac{5\pi}{18}+\dfrac{k2\pi}{3}\)
d.
\(cot4x=-\sqrt{3}\)
\(\Leftrightarrow4x=-\dfrac{\pi}{6}+k\pi\)
\(\Leftrightarrow x=-\dfrac{\pi}{24}+\dfrac{k\pi}{4}\)
