Ответ: 4.1) x = 2pi*k

x = 3pi + 4pi*k

4.2) x = -pi/8 + pi*k/2

5)см реш

Пошаговое объяснение:

4 -----------

1)

2 sin( x/2) = 1 - cosx

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

2sin(x/2) = 1 - 1 + sin^2(x/2) + sin^2(x/2)

2sin(x/2) = 2sin^2(x/2)

2sin(x/2)(1 - sinx/2) = 0

sin(x/2) = 0

sin(x/2) = -1

x/2 = pi*k

x/2 = 3pi/2 + 2pi*k

x = 2pi*k

x = 3pi + 4pi*k

k - целое число

2)

cos(3pi/2 + x)cos3x - cos(pi - x)sin3x = -1

sinxcos3x + cosxsin3x = -1

sin(4x)  = -1

4x = -pi/2 + 2pi*k

x = -pi/8 + pi*k/2

5--------------------------

(tga + ctga)(1 - cos4a) = (sina/cosa + cosa/sina)(1 - 1 + 2sin^2(2a)) =

2sin^2(2a)/sinacosa = 4sin^2(2a)/sin2a = 4sin(2a)