6sin^2(x+π/2)-5sin(x+π)-5=0
6сos²x+5sinx-5=0
6-6sin²x+5sinx-5=0
6sin²x-5sinx-1=0
sinx=a
6a²-5a-1=0
D=25+24=49
a1=(5+7)/12=1⇒sinx=1⇒x=π/2+2πk,k∈z
a2=(5-7)/12=-1/6⇒sinx=-1/6⇒x=-arcsin1/6+2πk U x=-π+arcsin1/6+2πk,k∈z
---------------------------------------
k=0⇒x=π/2
k=1⇒x=5π/2
k=1⇒x=2π-arcsin1/6
k=1⇒π+arcsin1/6