Упростить выражения: 1) [latex]cos( frac{ pi }{4} +a)*cos(frac{ pi }{4}-a)+ frac{1}{2}sin^2a[/latex] 2) [latex]cos3a+sina*sin2a[/latex] 3) [latex]cos2a-cosa*cos3a[/latex]

1) [latex]Cos( frac{ pi }{4}+ alpha )=Cos frac{ pi }{4}*Cos alpha -Sin frac{ pi }{4}*Sin alpha = frac{ sqrt{2} }{2}Cos alpha - frac{ sqrt{2}}{2}*Sin alpha [/latex][latex]Cos( frac{ pi }{4}- alpha )=Cos frac{ pi }{4}*Cos alpha +Sin frac{ pi }{4}*Sin alpha = frac{ sqrt{2} }{2}Cos alpha + frac{ sqrt{2}}{2}*Sin alpha[/latex][latex](frac{ sqrt{2} }{2}Cos alpha - frac{ sqrt{2}}{2}*Sin alpha)*(frac{ sqrt{2} }{2}Cos alpha + frac{ sqrt{2}}{2}*Sin alpha)+ frac{1}{2}Sin^{2} alpha = frac{1}{2}Cos^{2} alpha [/latex]2) Sinα*Sin2α=0,5 (Cos(-α)-Cos3α)Cos3α+0,5Cosα-0,5Cos3α=0,5(Cosα+Cos3α)=Cosα*Cos2α3) Cosα*Cos3α=0,5 (Cos(-2α)+Cos4α)Cos2α-0,5Cos2α-0,5Cos4α=0,5(Cos2α-Cos4α)=Sinα*Sin3α