1.
\(\Leftrightarrow cosx=\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow x=\pm\dfrac{\pi}{4}+k2\pi\)
2.
\(\Leftrightarrow\dfrac{\sqrt{3}}{2}sin2x-\dfrac{1}{2}cosx=-1\)
\(\Leftrightarrow sin\left(2x-\dfrac{\pi}{6}\right)=-1\)
\(\Leftrightarrow2x-\dfrac{\pi}{6}=-\dfrac{\pi}{2}+k2\pi\)
\(\Leftrightarrow2x=-\dfrac{\pi}{3}+k2\pi\)
\(\Leftrightarrow x=-\dfrac{\pi}{6}+k\pi\)
3.
\(\Leftrightarrow\dfrac{3}{5}sin3x+\dfrac{4}{5}sin3x=1\)
Đặt \(\dfrac{3}{5}=cosa\) với \(a\in\left(0;\dfrac{\pi}{2}\right)\Rightarrow\dfrac{4}{5}=sina\)
Pt trở thành:
\(sin3x.cosa+cos3x.sina=1\)
\(\Leftrightarrow sin\left(3x+a\right)=1\)
\(\Leftrightarrow3x+a=\dfrac{\pi}{2}+k2\pi\)
\(\Leftrightarrow x=-\dfrac{a}{3}+\dfrac{\pi}{6}+\dfrac{k2\pi}{3}\)
4.
\(\Leftrightarrow\left[{}\begin{matrix}cosx=1\\cosx=\dfrac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k2\pi\\x=\pm\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\)
