Имеем: tg^2 x=(1-cos 2x)/(1+cos 2x), sin^2 x=(1-cos 2x)/2. Подставим эти значения:24×(1-cos 2x)/(1+cos 2x)-9×(1-cos 2x)/2=2, (2×24×(1-cos 2x)-9×(1-cos 2x)×(1+cos 2x))/(2×(1+cos 2x))=2, 48-48cos 2x-9×(1-cos^2 2x)=2×2×(1+cos 2x), 48-48cos 2x-9+9cos^2 2x=4+4cos 2x, 9cos^2 2x-52cos 2x+35=0. Пускай cos 2x =y, имеем 9у^2-52у+35=0, D=(-52)^2-4×9×35=2704-1260=1444, y1=(52-корень из 1444)/(2×9)=(52-38)/18=14/18=7/9, х2=(52+корень из 1444)/(2×9)=(52+38)/18=90/18=5. cos 2x=y. При cos 2x=7/9, tg^2 x=(1-7/9)/(1+7/9)=(2/9)/(16/9)=1/8, tg x1=1/(2 корень из 2), tg x2=-1/(2 корень из 2). При cos 2x=7/9, sin^2 x=(1-7/9)/2=(2/9)/2=1/9, sin x1=-1/3, sin x2=1/3. При cos 2x=5, tg^2 x=(1-5)/(1+5)=4/6=2/3, tg x3=-корень из 2/3, tg x4=+корень из 2/3. sin^2 x=(1-5)/2=-2.
log(1/3) (x) + 2 = 3*log(1/3) (x)
log(1/3) (x) + 2 = 3*log(1/3) (x)
3*log(1/3) (x) - log(1/3) (x) = 2
log (1/3) (x)^3 - log(1/3) (x) = 2
log (1/3) ((x)^3) / (x)) = 2
x^2 = (1/3)^2
x^2 = (1/9)
x1 = -1/3
x2 = 1/3