1000−10y−y²+y³ = 10³+y³ −10y−y² = (10+у)(10²-10у+у²)-у(10+у) =
= (10+у)((10²-10у+у²)-у) = (10+у)(100-10у+у²-у) = (10+у)(у²-11у+100)
105)
1) sin²x + sin²2x = 1
sin²2x - cos²x = 0
(sin2x - cosx)(sin2x + cosx) = 0
cos²x(2sinx - 1)(2sinx + 1) = 0
cosx = 0 => x = π/2 + πn
sinx = ±½ => x = ±π/6 + 2πn; x = ±5π/6 + 2πn
2) sin²x + cos²2x = 1
cos²2x - cos²x = 0
(2cos²x - 1)² - cos²x = 0
(2cos²x - cosx - 1)(2cos²x + cosx - 1) = 0
t = cosx
(2t² - t - 1)(2t² + t - 1) = 0
t = ±½; t = ±1
cosx = 1 => x = 2πn
cosx = -1 => x = π + 2πn
cosx = ½ => x = ±π/3 + 2πn
cosx = -½ => x = π ± π/3 + 2πn
Остальные сорь... С ходу не решаются что-то
Y = y(π/6) + y'(π/6)*(x - π/6) - уравнение касательной
Y || y=x, значит у касательной коэффициент перед х равен 1, k=y'=1
Y = a*sin(π/6) + a + x - π/6 = x + (1.5a - π/6)
y'(π/6) = a*cos(π/6) = a√3/2 = 1, a=2/√3 = 2√3/3
Y = x + (3*2√3/2*3) - π/6 = x + √3 - π/6
sin^2a/cos^2a-sin^2a=sim^2a(1-cos^2a)/cos^2a=sin^2a*sin^2a/cos^2a=tg^2a*sin^2a
1-tg^2a+tg^4a/cos^2a=1-sin^2a/cos^2a+tg^4a/cos^2a=(cos2a+tg^4a)/cos^2a