a) 2cos^2 2x +cos2 x =2sin^2x +1/2 b) 2sin^2 3x +2 =(cos2x+1)(4sin2x-1)
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\(\begin{array}{l} a)2{\cos ^2}2x + \cos 2x = 2{\sin ^2}x + \frac{1}{2}\\ \Rightarrow 2{\cos ^2}2x + \cos 2x = 1 - \cos 2x + \frac{1}{2}\\ \Rightarrow 2{\cos ^2}2x + 2\cos 2x - \frac{3}{2} = 0\\ \Rightarrow \left[ \begin{array}{l} \cos x = \frac{1}{2}\\ \cos x = \frac{{ - 3}}{2} < - 1(l) \end{array} \right.\\ \Rightarrow x = \pm \frac{\pi }{3} + k2\pi (k \in ) \end{array}\)
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