Question

а) 2cos(x+pi/2)=-1
б) sin(-2x)=1

Answer 1

N1

2cos(x + π/2) = -1

cos(x + π/2) = -1/2

[x + π/2 = 2π/3 + 2πn

[x + π/2 = -2π/3 + 2πn

[x = π/6 + 2πn

[x = -7π/6 + 2πn n € Z

Ответ : x = π/6 + 2πn ; x = -7π/6 + 2πn ; n € Z

N2

sin(-2x) = 1

-sin2x = 1

sin2x = -1

2x = -π/2 + 2πk

x = -π/4 + πk ; k € Z

Ответ : -π/4 + πk ; k € Z