Cos^2(15)-sin^2(15)=cos(2*15)=cos(30) = корень(3)/2
cos(pi-a)=- cos(a)
sin(120) = sin(180-60)=sin(60) = корень(3)/2
(1+cos(2a))*sin(a)/cos(a) = ((cos^2(a)+sin^2(a))+cos^2(a)-sin^2(a))*sin(a)/cos(a) =
=2*cos^2(a)*sin(a)/cos(a) = 2*cos(a)*sin(a) = sin(2a)
(sin(8a)-sin(2a))(cos(2a)-cos(8a))/(1-cos(6a)) = (2*sin(3a)*cos(5a))(2*sin(3a)*sin(5a))/(cos^2(3a)+sin^2(3a)-cos^2(3a)+sin^2(3a)) =
= 4sin^2(3a)*cos(5a)*sin(5a))/(2sin^2(3a)) = 2cos(5a)*sin(5a)= sin(10a)
6 1 Г
6 2 В
6 3 А
6 4 Д
4cos(x)+5*sin(x) = корень(4^2+5^2)*sin(x+arccsin(4/корень(4^2+5^2))
минимальное значение - корень(4^2+5^2)= - корень(41)
максимальное значение + корень(4^2+5^2)= + корень(41)
1-cos(a) - sin(a) = 2*корень(2)*sin(a/2)*sin(a/2-pi/4) - доказать
cos(a)=cos^2(a/2)-sin^2(a/2)
sin(a) = 2sin(a/2)cos(a/2)
1=cos^2(a/2)+sin^2(a/2)
1-cos(a) - sin(a)=cos^2(a/2)+sin^2(a/2)-cos^2(a/2)+sin^2(a/2)-2sin(a/2)cos(a/2)=
=2sin^2(a/2)-2sin(a/2)cos(a/2)=2sin(a/2)(sin(a/2)-cos(a/2))=2sin(a/2)(sin(a/2)-sin(pi/2-a/2))=
=2sin(a/2)(sin(a/2)+sin(a/2-pi/2))=(формула сумма синусов)=
=2sin(a/2)(2*sin(a/2+pi/4)*cos(-pi/4))=2sin(a/2)(2*sin(a/2+pi/4)*корень(2)/2)) =
=2sin(a/2)(sin(a/2+pi/4)*корень(2) - доказано