TeAnte
Просветленный
(40485)
4 дня назад
sin²x + cos²x = 1
Sin²x - 2sinxcosx - 3cos²x = 0
Sin²x - 2sinxcosx = 3cos²x
2sin²x - 2sinxcosx = 3cos²x + sin²x
2(sin²x - sinxcosx) = 3cos²x + sin²x
2(sin²x - sinxcosx) = 3cos²x + (1 - cos²x)
2(sin²x - sinxcosx) = 2cos²x + 1
sin²x - sinxcosx = cos²x + 1/2
sinx(sinx - cosx) = cos²x + 1/2
sinx(sinx - cosx) + cos²x = 3/2
(sinx - cosx)(sinx + cosx) = 3/2
sinx + cosx = √2 sin(x + π/4)
(sinx - cosx)√2 sin(x + π/4) = 3/2
sinx - cosx = 3/(2√2 sin(x + π/4))
sin(x + π/4) = ±√3/2
Ответ: x = -π/4 + arcsin(±√3/2) + 2πn
Как видете всё очень просто