1) (sina + cosa) ^2 + (sina - cosa) ^2=

2) 3cosx = - 2sin^2x=

1) (sina + cosa) ^2 + (sina - cosa) ^2=sin (a) ^2 + 2*sin (a) * cos (a) + cos (a) ^2 + sin (a) ^2 - 2*sin (a) * cos (a) + cos (a) ^2 = 2 * (sin (a) ^2 + cos (a) ^2) = 2

2) 3cos (x) = - 2sin (x) ^2

3cos (x) + 2 = 2 (1 - sin (x) ^2)

3cos (x) + 2 = 2cos (x) ^2

2cos (x) ^2 - 3cos (x) - 2 = 0

Пусть cos (x) = t, тогда получим квадратное уравнение относительно t:

2t^2 - 3t - 2 = 0

D = (-3) ^2 - 4*2 * (-2) = 25

t1,2 = (3 + - √25) / 2 = (3+-5) / 2

t1 = (3-5) / 2 = - 1

t2 = (3+5) / 2 = 4 - не подходит в силу ограничений на область значений cos (x)

Тогда cos (x) = - 1, x = π + 2πn, n∈Z