trygonometria Agata: Rozwiąż równanie: cos2x+sin²2x=1

olekturbo: cos²x−sin²x+sin²2x = 1 cos²x−sin²x+(2sinxcosx)² = 1 cos²x−sin²x+4sin²xcos²x = 1 (1−sin²x)−sin²x+4sin²x(1−sin²x) = 1 1−sin²x−sin²x+4sin²x−4sin⁴x = 1 2sin²x−4sin⁴x = 0 sin²x−2sin⁴x = 0 t = sin²x t−2t² = 0 t(1−2t) = 0 t = 0 v 1−2t = 0 1 = 2t

	1
t =
	2

	1
t1 = 0 v t2 =
	2

sin²x = 0 x = 0 + k*180

	1
sin2x =
	2

	√2
x =
	2

x = 60 + k*360 v x = 120 + k*360