1)+)$sin^4x+cos^4x=1-2sin^2xcos^2x=1-\frac{1}{2}sin^22x$
+)$cot(x+\frac{\pi}{3})cot(\frac{\pi}{6}-x)=cot(x+\frac{\pi}{3})tan(x+\frac{\pi}{3})=1$
pt$\Leftrightarrow1-\frac{1}{2}sin^22x=\frac{7}{8}\Leftrightarrow \frac{1}{2}sin^22x= \frac{1}{8}\Leftrightarrow sin2x=\pm \frac{1}{2}$
2)
VT=$\frac{3sinx-sin3x}{4}cos3x+\frac{3cosx+cos3x}{4}sin3x$
$=\frac{3}{4}(sinxcos3x+cosxsin3x)=\frac{3}{4}sin4x$
p$t\Leftrightarrow \frac{3}{4}sin4x=sin^34x\Leftrightarrow sin4x(sin^24x-\frac{3}{4})=0$