1-4sin^2t*cos^2t / (sint+cost) ^2+2sint*cost=1

Во всей вероятности

(1 - 4sin²t·cos²t) / (sint+cost) ² + 2sint·cost) = 1

(1 - sin2t) ² / (1+2sint·cost) + sin2t = 1

1 - sin2t + sin2t + (sin2t) ² = 1+sin2t;

(sin2t) ² - sin2t = 0

sin2t· (sin2t - 1) = 0

a) sin2t = 0 ⇒ 2t = πk ⇒ t = π/2 ·k; k∈Z

b) sin2t = 1 ⇒ 2t = 2πm + π/2 ⇒ t=πm + π/4; m∈Z