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
б) 36х^2 -12ху + у^2 = (6х)^2 - 2•6ху + у^2 =
= (6х-у)^2
в) m^2 + 2mn + n^2 = (m+n)^2
г) a²-2ab+b² = (a-b)^2
д) y²-36 = (y^2 - 6^2) = (y+6)(y-6)
е) x²-0,16y² = x^2 - (0,4y)^2 = (x+0,4y)(x-0,4y)
ё) a^6-25 = (a^3)^2 - 5^2 = (a^3 + 5)(a^3 - 5)
ж) 400-y² = 20^2 - y^2 = (20+y)(20-y)