Решите тригонометрическое уравнение:

Question

Решите тригонометрическое уравнение:

Answer 1

(1-cos2x)/2+(1-cos4x)/2=(1+cos6x)/2+(1+cos8x)/2
1+cos6x+1+cos8x-1+cos2x-1+cos4x=0
(cos6x+cos4x)+(cos8x+cos2x)=0
2cos5xcosx+2cos5xcos3x=0
2cos5x(cosx+cos3x)=0
2cos5x*2cos2xcosx=0
cos5x=0⇒5x=π/25+πn⇒x=π/10+πn/5,n∈z
cos2x=0⇒2x=π/2+πk⇒x=π/4+πk/2
cosx=0⇒x=πm,m∈z

Comments

cosx=0⇒x=π/2 + πm,m∈z