Sin30*ctg30-cos30cos^2L*tg^2L+sin^2L*ctg^2L1+sin(П+2)*cos(3П/2+L)(1-sin30)*(1+sin30)+(1+cos30)(1-cos30)

1). [latex]sin 30^{\circ}*ctg 30^{\circ} - cos 30^{\circ} = sin 30^{\circ}* \frac{cos 30^{\circ}}{sin 30^{\circ}} - cos 30^{\circ} =[/latex] [latex]=cos 30^{\circ} - cos 30^{\circ} = 0[/latex] 2). [latex]cos^{2} \alpha *tg^{2} \alpha +sin^{2} \alpha *ctg^{2} \alpha =sin^{2} \alpha +cos^{2} \alpha =1[/latex] 3). [latex]1+sin( \pi + \alpha )*cos(\frac{3 \pi }{2}+ \alpha) =1-sin \alpha *sin \alpha =cos^{2} \alpha [/latex] 4). [latex](1-sin30^{\circ})(1+sin30^{\circ}) +(1+cos30^{\circ})(1-cos30^{\circ}) =[/latex] [latex]= 1-sin^{2}30^{\circ}+1-cos^{2} 30^{\circ} = 2-1=1[/latex]