Question

Решите тригонометрическое уравнение: $sqrt{3} cos ^{2} x -0.5sin2x=0$
$cos ^{2}x+sin2x=0$

Answer 1

1
√3cos²x-sinxcosx=0
cosx(√3cosx-sinx)=0
cosx=0⇒x=π/2+πn,n∈z
√3cosx-sinx=0/cosx
√3-tgx=0
tgx=√3⇒x=π/3+πk,k∈z
2
cos²x+2sinxcosx=0
cosx(cosx+2sinx)=0
cosx+2sinx=0/cosx
1+2tgx=0
tgx=-1/2⇒x=-arctg1/2+πk,k∈z
cosx=0⇒x=π/2+πn,n∈z