Question

Решить уравнение sin5x=cos7x
на промежутке:

Answer 1

sin5x-sin(π/2-7x)=0
2sin(6x-π/4)cos(π/4-x)=0
sin(6x-π/4)=0⇒6x-π/4=πn⇒6x=π/4+πn⇒x=π/24+πn/6
cos(π/4-x)=0⇒cos(x-π/4)=0⇒x-π/4=π/2+πn⇒x=3π/4+πn
x=21π/4;23π/4∈[5π;6π]