Question

Тригонометрические уравнения.
1). sin3x=cos5x
2). 1+2sin*Пх/3=0(2<х<4)

Answer 1

1)sin3x-cos5x=0
sin3x-sin(π/2-5x)=0
2sin(4x-π/4)cos(π/4-x)=0
sin(4x-π/4)=0⇒4x-π/4=πn⇒4x=π/4+πn⇒x-π/16+πn/4
cos(π/4-x)=0⇒π/4-x=π/2+πn⇒x=-π/2+πn
2)sinπx/3=-1/2
πx/3=(-1)^n+1*π/6+πn
x=(-1)^n+1*1/2+3n
x=3,5