Question

Решите уравнение -sinx/2=cosx

Answer 1

-sin(x/2) = cos x = 1 - 2sin^2(x/2)
Замена sin(x/2) = y
2y^2 - y - 1 = 0
(y - 1)(2y + 1) = 0
y1 = sin(x/2) = -1/2
x/2 = -pi/6 + 2pi*k; x1 = -pi/3 + 4pi*k
x/2 = -5pi/6 + 2pi*k; x2 = -5pi/3 + 4pi*k

y2 = sin(x/2) = 1
x3 = pi/2 + 2pi*n