10.
\(\Leftrightarrow coss7x.cos5x+sin7x.sin5x-\sqrt{3}sin2x=1\)
\(\Leftrightarrow cos\left(7x-5x\right)-\sqrt{3}sin2x=1\)
\(\Leftrightarrow\dfrac{1}{2}cos2x-\dfrac{\sqrt{3}}{2}sin2x=\dfrac{1}{2}\)
\(\Leftrightarrow cos\left(2x+\dfrac{\pi}{3}\right)=cos\left(\dfrac{\pi}{3}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+\dfrac{\pi}{3}=\dfrac{\pi}{3}+k2\pi\\2x+\dfrac{\pi}{3}=-\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k\pi\\x=-\dfrac{\pi}{3}+k\pi\end{matrix}\right.\)
11.
\(\Leftrightarrow2\sqrt{2}sinx.cosx+2\sqrt{2}cos^2x=3+cos2x\)
\(\Leftrightarrow\sqrt{2}sin2x+\sqrt{2}\left(1+cos2x\right)-cos2x=3\)
\(\Leftrightarrow\sqrt{2}sin2x+\left(\sqrt{2}-1\right)cos2x=3-\sqrt{2}\)
Pt lượng giác bậc nhất có: \(\left(\sqrt{2}\right)^2+\left(\sqrt{2}-1\right)^2< \left(3-\sqrt{2}\right)^2\) nên vô nghiệm
