1. Решить уравнения:

а) sin x/2 = 1/2

б) 2cos^2x - sin x - 1 = 0

в) 2cos^2x - sin x - 1 = 0

2. Найти cos a, если sina = √3/2 и п/4

A) x/2 = (-1) ^k*arcsin (1/2) + πk

x = ((-1) ^k * (π/6) + πk) / 2

B) 2*cos^2x - sinx - 1 = 0

2 * ((1+cos2x) / 2) - sinx - 1 = 0

Раскроем скобки

1 + cos2x - sinx - 1 = 0

Cos2x = 1 - 2sin^2x

1 - 2sin^2x - sinx = 0

Sinx = t

2t^2 + t - 1 = 0

t1 = - 1 t2 = 1/2

Sinx = - 1 sinx = 1/2

X1 = (-1) ^k * (3π/2) + πk

X2 = (-1) ^k * (π/6) + πk