cos5x-sin5x=sin7x-cos7x

Question

cos5x-sin5x=sin7x-cos7x

Answer 1

Решение:
cos5x-sin5x=sin7x-cos7x 
cos5x+cos7x=sin5x+sin7x
2сos6x*cosx=2sin6x*cosx
сos6x*cosx-sin6x*cosx=0
cosx(cos6x-sin6x)=0
a) cosx=0
x1=π/2+πn
cos6x-sin6x=0
tg6x=1
6x=π/4+πn
x2=π/24+πn/6

Answer 2

Cos5x-sin5x=sin7x-cos7x 
cos5x+cos7x=sin5x+sin7x
2сos6x*cosx=2sin6x*cosx
сos6x*cosx-sin6x*cosx=0
cosx(cos6x-sin6x)=0
a) cosx=0
x1=π/2+πn
cos6x-sin6x=0
tg6x=1
6x=π/4+πn
x2=π/24+πn/6