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]