a.
\(cos^2\frac{x}{2}+sin^2\frac{x}{2}-2sin\frac{x}{2}cos\frac{x}{2}+\sqrt{3}cosx=2\)
\(\Leftrightarrow1-sinx+\sqrt{3}cosx=2\)
\(\Leftrightarrow\frac{\sqrt{3}}{2}cosx-\frac{1}{2}sinx=\frac{1}{2}\)
\(\Leftrightarrow cos\left(x+\frac{\pi}{6}\right)=\frac{1}{2}\)
\(\Leftrightarrow...\)
b.
\(cos5x-cos3x+1-cos4x=0\)
\(\Leftrightarrow-2sin4x.sinx+2sin^22x=0\)
\(\Leftrightarrow2sin2x.cos2x.sinx-sin^22x=0\)
\(\Leftrightarrow sin2x\left(2sinx.cos2x-sin2x\right)=0\)
\(\Leftrightarrow sin2x\left(2sinx.cos2x-2sinx.cosx\right)=0\)
\(\Leftrightarrow2sinx.sin2x\left(cos2x-cosx\right)=0\)
\(\Leftrightarrow...\)
c.
\(4cosx.cos3x+2\sqrt{3}sinx.cosx+2cos^2x-1=-1\)
\(\Leftrightarrow cosx\left(2cos3x+\sqrt{3}sinx+cosx\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\Leftrightarrow...\\2cos3x+\sqrt{3}sinx+cosx=0\left(1\right)\end{matrix}\right.\)
Xét (1)
\(\Leftrightarrow\frac{\sqrt{3}}{2}sinx+\frac{1}{2}cosx=-cos3x\)
\(\Leftrightarrow sin\left(x+\frac{\pi}{6}\right)=sin\left(3x-\frac{\pi}{2}\right)\)
\(\Leftrightarrow...\)
