Question

Решить уравнение 5sin4x-cos2x=0

Answer 1

5sin4x-cos2x=0;⇒
10sin2xcos2-cos2x=0;⇒
cos2x(10sin2x -1)=0;
cos2x=0;⇒2x=π/2+nπ;n∈Z;⇒
x=π/4+n·π/2;n∈Z;
10sin2x=1;⇒sin2x=1/10;⇒2x=(-1)ⁿ·arcsin(1/10)+nπ;n∈Z;⇒
x=(-1)ⁿ·[arcsin(1/10)+nπ]/2;n∈Z;