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*Cos2α 3) Cosα*Cos3α=0,5 (Cos(-2α)+Cos4α) Cos2α-0,5Cos2α-0,5Cos4α=0,5(Cos2α-Cos4α)=Sinα*Sin3α