Question

помогите с тригонометрией

Answer 1

ctgx⋅cos5x=cos6x+sin5x 
ctgx⋅cos5x=cos5xcosx-sin5xsin+sin5x 
cos5x(cosx⋅(1-sinxsinx)=sin5x(1-sinx) 

1)sinx=1⇔ x=π2+2πn,n∈Z 

cos5x⋅cosx=sin5x⋅sinx 
(cos4x+cos6x2)=(cos4x-cos6x2) 

2)cos6x=0,⇔6x=π2+πk x=π12+πk6,k∈Z 

2 
Ctg(x/2) = Cos(x/2) / Sin(x/2) 
Sin(x) = 2Sin(x/2)*Cos(x/2) 

Sin(x)+ctg(x/2)=2 
2Sin(x/2)*Cos(x/2) + Cos(x/2) / Sin(x/2) = 2 
{Cos(x/2){2Sin^2(x/2) + 1} } / Sin(x/2) = 2