Kak takoe resyt? sin4x-sin2x=sinx

Question

Kak takoe resyt?

sin4x-sin2x=sinx

Answer 1

sin4x=sin2x;

2sin2xcos2x-sin2x=0;

sin2x(2cos2x-1)=0;

sin2x=0;

2x=πn. n∈Z.

x=πn/2. n∈Z.

cos2x=0,5;

2x=±π/3+2πn. n∈Z.

x=±π/6+πn. n∈Z.

Answer 2

sin*4*x=sin*2*x;

2*sin*2*x*cos*2*x-sin*2*x=0;

sin2*x*(2*cos*2*x-1)=0;

sin*2*x=0;

2*x=π*n. n∈Z.

x=π*n/2. n∈Z.

cos*2*x=0,5;

2*x=±π/3+2*π*n. n∈Z.

x=±π/6+π*n. n∈Z.