$\begin{array}{l}a)\,\,4\sin^23x = 1\\ \Leftrightarrow 2(1 - \cos6x) = 1\\ \Leftrightarrow \cos6x = \dfrac{1}{2}\\ \Leftrightarrow 6x = \pm \dfrac{\pi}{3} + k2\pi\\ \Leftrightarrow x = \pm \dfrac{\pi}{18} + k\dfrac{\pi}{3}\quad (k \in \Bbb Z)\\ c)\,\,4\sin^24x = 3\\ \Leftrightarrow 2(1 - \cos8x) = 3\\ \Leftrightarrow \cos8x = - \dfrac{1}{2}\\ \Leftrightarrow 8x = \pm \dfrac{2\pi}{3} + k2\pi\\ \Leftrightarrow x = \pm \dfrac{\pi}{12} + k\dfrac{\pi}{4}\quad (k \in \Bbb Z)\\ e)\,\,4\cos^22x = 3\\ \Leftrightarrow 2(1 + \cos4x) = 3\\ \Leftrightarrow \cos4x = \dfrac{1}{2}\\ \Leftrightarrow 4x = \pm \dfrac{\pi}{3} + k2\pi\\ \Leftrightarrow x = \pm \dfrac{\pi}{12} +k\dfrac{\pi}{2} \quad (k \in \Bbb Z) \end{array}$
