Докажи равенства 1) {\cos ^2 \bigg( x+\cfrac{\pi}{6} \bigg) \,\mathrlap{\,-}} {- \cos \bigg( x+\cfrac{\pi}{6} \bigg) \cos \bigg( x-\cfrac{\pi}{6} \bigg) \,\mathrlap{\,+}} {+ \cos ^2 \bigg( x-\cfrac{\pi}{6} \bigg) =0,75}. 2) {\sin ^2 \bigg( x+\cfrac{\pi}{4} \bigg) - \sin ^2 \bigg( x-\cfrac{\pi}{6} \bigg) \,\mathrlap{\,-}} {-\sin \cfrac{\pi}{12} \cos \bigg( 2x+\cfrac{\pi}{12} \bigg)=\sin 2x}.

Задание

Докажи равенства

\({\cos ^2 \bigg( x+\cfrac{\pi}{6} \bigg) \,\mathrlap{\,-}}\) \({- \cos \bigg( x+\cfrac{\pi}{6} \bigg) \cos \bigg( x-\cfrac{\pi}{6} \bigg) \,\mathrlap{\,+}}\) \({+ \cos ^2 \bigg( x-\cfrac{\pi}{6} \bigg) =0,75}\) .
\({\sin ^2 \bigg( x+\cfrac{\pi}{4} \bigg) - \sin ^2 \bigg( x-\cfrac{\pi}{6} \bigg) \,\mathrlap{\,-}}\) \({-\sin \cfrac{\pi}{12} \cos \bigg( 2x+\cfrac{\pi}{12} \bigg)=\sin 2x}\) .