2)cos2α+2sin²α=cos²α-sin²α+sin²α+sin²α=
=(cos²α+sin²α)-sin²α+sin²α=1;
1-sin2α·cosα/2sinα=1-2sinα·cosα·cosα/2sinα=
=1-cos²α=sin²α;
3)sin40⁰+cos70⁰-cos10⁰=0
sin40⁰+(-2sin[(70⁰+10⁰)/2]sin[(70⁰-10⁰)/2])=
=sin40⁰-2sin40⁰sin30⁰=sin40⁰-2sin40⁰·1/2=sin40⁰-sin40⁰=0
4)sinα-sin(π/3-α)=2sin(α-π/3+α)/2·cos(α+π/3-α)/2=
=2sin(α-π/6)·cosπ/6=2·sin(α-π/6)·√3/2=√3·sin(α-π/6)
X(y-5)-6y(5-y)=x(y-5)+6y(y-5)=(y-5)(x+6y)
Естественно больше .
7х^2+3= 10х^2
4sin210°-3√2cos(-135°)=4sin(180°+30°)+3√2cos(90°+45°)=
= -4sin30°-3√2cos45°=-4.0,5-3√2.√2/2=-2-3=-5
Otvet: -5
( cos(-x)=cosx, sin(-x)=-sinx, sin30°=0,5, cos45°=(√2)/2 )
У=1-4sinx=sin²x/2-4sinx/2*cosx/2+cos²x/2
=(sinx/2-cosx/2)²=(cos(π/2-x/2)-cosx/2)²=
-2sinπ/4*sin(π/2-x/2-x/2)/2
-2√2/2*sin(π/4-x/2)=
-√2*sin(π/4-x/2)
sin(π/4-x/2)€[-1;1]
-√2*sin(π/4-x/2)€[-√2;√2]
множество значений функции
[-√2;√2]