a,
PT\(\Leftrightarrow sin^22x-cos^28x=sin\left(10x+\dfrac{\pi}{2}\right)\)
\(\Leftrightarrow sin^22x-cos^28x=cos10x\)
\(\Leftrightarrow\dfrac{1-cos4x}{2}-\dfrac{1+cos16x}{2}=cos10x\)
\(\Leftrightarrow-cos4x-cos16x=2cos10x\)
\(\Leftrightarrow-2.cos10x.cos6x=2cos10x\)
\(\Leftrightarrow cos10x+cos10x.cos6x=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos10x=0\\1+cos6x=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}cos10x=0\\cos6x=-1\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{20}+\dfrac{k\pi}{10}\\x=\dfrac{\pi}{6}+\dfrac{k\pi}{3}\end{matrix}\right.\) , \(k\in Z\)
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c) Pt\(\Leftrightarrow\dfrac{1+cos2x}{2}=cos\dfrac{4x}{3}\)
\(\Leftrightarrow1+cos2x-2cos\dfrac{4x}{3}=0\)
Đặt \(t=\dfrac{2x}{3}\). Pttt \(1+cos3t-2cos2t=0\)
\(\Leftrightarrow1+4cos^3t-3cost-2\left(2cos^2t-1\right)=0\)
\(\Leftrightarrow4cos^3t-4cos^2t-3cost+3=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cost=1\\cost=\dfrac{\sqrt{3}}{2}\\cost=-\dfrac{\sqrt{3}}{2}\end{matrix}\right.\)
TH1:\(cost=1\Leftrightarrow t=k2\pi\)\(\Leftrightarrow\dfrac{2x}{3}=k2\pi\)\(\Leftrightarrow x=k3\pi\) (\(k\in Z\))
TH2:\(cost=\dfrac{\sqrt{3}}{2}\Leftrightarrow t=\pm\dfrac{\pi}{6}+k2\pi\)\(\Leftrightarrow x=\pm\dfrac{\pi}{4}+k3\pi\)\(\left(k\in Z\right)\)
TH3:\(cost=-\dfrac{\sqrt{3}}{2}\Leftrightarrow t=\pm\dfrac{5\pi}{6}+k2\pi\)\(\Leftrightarrow x=\pm\dfrac{5\pi}{4}+k3\pi\)\(\left(k\in Z\right)\)
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