1) sin a = √2/2; a1 = pi/4+2pi*k; cos a1 = √2/2
a2 = 3pi/4+2pi*k; cos a2 = -√2/2
cos(60 + a1) = cos 60*cos a1 - sin 60*sin a1 =
= 1/2*√2/2 - √3/2*√2/2 = √2/4*(1 - √3) = -√2(√3 - 1)/4
cos(60 + a2) = cos 60*cos a2 - sin 60*sin a2 =
= -1/2*√2/2 - √3/2*√2/2 = -√2/4*(1 + √3) = -√2(√3 + 1)/4
2) sin a = 2/3; cos b = -3/4; a ∈ (pi/2; pi); b ∈ (pi; 3pi/2)
cos a < 0; sin^2 a = 4/9; cos^2 a = 1-4/9 = 5/9; cos a = -√5/3
sin b < 0; cos^2 b = 9/16; sin^2 b = 1-9/16 = 7/16; sin b = -√7/4
sin(a+b) = sin a*cos b + cos a*sin b =
= 2/3*(-3/4) + (-√5/3)(-√7/4) = -6/12 + √35/12 = (√35 - 6)/12
cos(-b) = cos b = -3/4
M<em>²-25-5-m=m²-m-30=(м-6)(м+5)
по теореме виетта
m1+m2=1
м1*м2=30
м1=6
м2=-5
</em>
4^[x+8] = 9*2^[x]
1/9 * 2^[x+16] = 1
2^[x+16] = 9
x+16=log2(9)
x=log2(9/65536)
Y= -2tg4x
y(-x)= -2tg4(-x)=2tg4x=-f(x) => f(x)=-2tg4x - нечётная
y= -2tg4x
y=-2tg4(x+T)=-2tg(4x+4T)
4T=П
Т=П/4 - наименьший положительный период