a)
Đặt \(t=x-\dfrac{\pi}{6}\)
Pttt: \(sin2t=5sint+cos\left(3t-\dfrac{\pi}{2}\right)\)
\(\Leftrightarrow sin2t=5sint+sin3t\)
\(\Leftrightarrow sin2t-sin3t=5sint\)
\(\Leftrightarrow2.sint.cost+4sin^3t-3sint=5sint\)
\(\Leftrightarrow sint.cost+2sin^3t-4sint=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sint=0\\cost+2sin^2t-4=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}sint=0\\-2cos^2t+cost-2=0\left(vn\right)\end{matrix}\right.\)\(\Leftrightarrow t=k\pi\left(k\in Z\right)\)
\(\Rightarrow x=\dfrac{\pi}{6}+k\pi\left(k\in Z\right)\)
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c,
Đặt \(t=x+\dfrac{\pi}{3}\)
Pttt: \(8cos^3t=cos\left(3t-\pi\right)\)
\(\Leftrightarrow8cos^3t=-cos3t\)\(\Leftrightarrow8cos^3t=3cost-4cos^3t\)
\(\Leftrightarrow4cos^3t-cost=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cost=0\\cost=\pm\dfrac{1}{2}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}t=\dfrac{\pi}{2}+k\pi\\t=\pm\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{6}+k\pi\\x=k2\pi\\x=-\dfrac{2\pi}{3}+k2\pi\end{matrix}\right.\)\(\left(k\in Z\right)\)
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