a.
\(\Leftrightarrow2-2cos\left(4x-2\right)=1\)
\(\Leftrightarrow cos\left(4x-2\right)=\dfrac{1}{2}\)
\(\Rightarrow\left[{}\begin{matrix}4x-2=\dfrac{\pi}{3}+k2\pi\\4x-2=-\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}+\dfrac{\pi}{12}+\dfrac{k\pi}{2}\\x=\dfrac{1}{2}-\dfrac{\pi}{12}+\dfrac{k\pi}{2}\end{matrix}\right.\)
b.
\(\Leftrightarrow\dfrac{1}{2}+\dfrac{1}{2}cos6x+\dfrac{1}{2}-\dfrac{1}{2}cos8x=1\)
\(\Leftrightarrow cos6x=cos8x\)
\(\Leftrightarrow\left[{}\begin{matrix}8x=6x+k2\pi\\8x=-6x+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k\pi\\x=\dfrac{k\pi}{7}\end{matrix}\right.\)
\(\Rightarrow x=\dfrac{k\pi}{7}\)
`a)4cos^2(2x-1)=1`
`<=>4[1+cos(4x-2)]/2=1`
`<=>2(1+cos(4x-2))=1`
`<=>2cos(4x-2)=-1`
`<=>cos(4x-2)=-1/2`
`<=>[(4x-2=[2\pi]/3+k2\pi),(4x-2=[-2\pi]/3+k2\pi):}`
`<=>[(x=1/2+\pi/6+k\pi/2),(x=1/2-\pi/6+k\pi/2):}` `(k in ZZ)`
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`c)cos^2 3x+sin^2 4x=1`
`<=>[1+cos 6x]/2+[1-cos 8x]/2=1`
`<=>1+cos 6x+1-cos 8x=2`
`<=>cos 8x=cos 6x`
`<=>[(8x=6x+k2\pi),(8x=-6x+k2\pi):}`
`<=>[(x=k\pi),(x=k\pi/7):}` `(k in ZZ)`
