3)(sin15+cos15)^2=1+sin30=1,5
4)а)tg105=tg(60+45)=sin(60+45)/cos(60+45)=(sin60*cos45+cos60*sin45)/(cos60*cos45-sin60*sin45)=(√3/2+1/2)*√2/2/(1/2-√3/2)√2/2=(√3/2+1/2)(1/2-√3/2)/(1/2-√3/2)^2=-1/2(1/4-√3/2+3/4)=-1/(2+√3)
в)ctg510=ctg(360+150)=ctg150=ctg(90+60)=tg60=√3
5)cos^2 2a+sin^2 2a=1
6)cos40-cos20=cos(30+10)-cos(30-10)=cos30*cos10-sin30*sin10-cos30*cos10-sin30*sin10=-2sin30*sin10=-sin10
sin20-cos40=sin(30-10)-cos(30+10)=sin30*cos10-sin10*cos30-cos30*cos10+sin30*sin10=1/2*cos10-sin10*√3/2-√3/2*cos10+1/2*sin10=1/2(sin10+cos10)-√3/2(sin10+cos10)=(1/2-√3/2)(sin10+cos10)=-((√3-1)/2)(sin10+cos10)
cos^4 x-6cos^2 x*sin^2 x+sin^4 x=cos4x
(cos^2 x-sin^2 x)^2-sin^2 2x=cos4x
cos^2 2x-sin^2 2x=cos4x