ОДЗ -sinx>0⇒sinx<0⇒x∈(π+2πn;2π+2πn) [log(11)(-sinx)=0⇒-sinx=1⇒sinx=-1⇒x=-π/2+2πn⇒x=3π/2+2πn [2cos²x-5cosx+2=0⇒x=5π/3+2πn cosx=a 2a²-5a+2=0 D=25-16=9 a1=(5-3)/4=1/2⇒cosx=1/2⇒x=+-π/3+2πn⇒x=5π/3+2πn a2=(5+3)/4=2⇒cosx=2>1 нет решения Ответ x=3π/2+2πn,x=5π/3+2πn,n∈z
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ОДЗ-sinx>0⇒sinx<0⇒x∈(π+2πn;2π+2πn)
[log(11)(-sinx)=0⇒-sinx=1⇒sinx=-1⇒x=-π/2+2πn⇒x=3π/2+2πn
[2cos²x-5cosx+2=0⇒x=5π/3+2πn
cosx=a
2a²-5a+2=0
D=25-16=9
a1=(5-3)/4=1/2⇒cosx=1/2⇒x=+-π/3+2πn⇒x=5π/3+2πn
a2=(5+3)/4=2⇒cosx=2>1 нет решения
Ответ x=3π/2+2πn,x=5π/3+2πn,n∈z