a) [latex]4sin^{2}(x- frac{ pi }{6})=3 \ sin^{2}(x- frac{ pi }{6} )= frac{3}{4} \ sin(x- frac{ pi }{6})= frac{ sqrt{3} }{2} \ sin(x- frac{ pi }{6} )=sin frac{ pi }{3} \ x- frac{ pi }{6} = frac{ pi }{3} +2k pi \ x= frac{ pi }{2} +2k pi \ lub \ x- frac{ pi }{6} = frac{2 pi }{3} +2k pi \ x= frac{5 pi }{6} +2k pi [/latex] b) [latex]2cos(2x- frac{ pi }{2} )=1 \ cos(2x- frac{ pi }{2} )= frac{1}{2} \ cos(2x- frac{ pi }{2} )=cos frac{ pi }{3} \ 2x- frac{ pi }{2} = frac{ pi }{3} +2k pi \ 2x= frac{5 pi }{6} +2k pi \ x= frac{5 pi }{12} +k pi \ lub \ 2x- frac{ pi }{2} =- frac{ pi }{3} +2k pi \ 2x= frac{ pi }{6} +2k pi \ x= frac{ pi }{12} +k pi [/latex] c) [latex]sin(3x- frac{ pi }{6} )= frac{ sqrt{3} }{2} \ sin(3x- frac{ pi }{6} )=sin frac{ pi }{3} \ 3x- frac{ pi }{6} = frac{ pi }{3} +2k pi \ 3x= frac{ pi }{2} +2k pi \ x= frac{ pi }{6} + frac{2k pi }{3} \ lub \ 3x- frac{ pi }{6}= frac{2 pi }{3} +2k pi \ 3x= frac{5 pi }{6} +2k pi \ x= frac{5 pi }{18} + frac{2k pi }{3} [/latex]
