Question

решите уравнение
$\sin {}^{2} x + \sin2x = 1$
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Answer 1

Ответ:

x = π/2 + πk , k € Z

x = arctg(1/2) + πk , k € Z

Пошаговое объяснение:

sin^2x + sin2x = 1

sin^2x + 2sinxcosx - 1 = 0

sin^2x + 2sinxcosx - (sin^2x + cos^2x) = 0 sin^2x + 2sinxcosx - sin^2x - cos^2x = 0 2sinxcosx - cos^2x = 0

cosx(2sinx - cosx) = 0

cosx = 0

x = π/2 + πk , k € Z

2sinx - cosx = 0

При косинус не равном 0

2sinx = cosx / : cosx

2tgx = 1 / :2

tgx = 1/2

x = arctg(1/2) + πk , k € Z