Question

Доказать тождества: 1. 1-cos(п-2 х)-cos(п+4 х)+cos(2п-6х)=4cоsх*соs2х*соs3х 2. 2*(1+cosх) - sin^2х=4cos^4 (х/2)

Answer 1

1. 1-cos(п-2х)-cos(п+4х)+cos(2п-6х)=4cоsх*соs2х*соs3х
1-cos(п-2х)-cos(п+4х)+cos(2п-6х)=cos6x+cos4x+cos2x+1
cos6x+cos4x+cos2x+1=4cosx*cos2x*cos3x
2.2*(1+cosх)-sin^2х=4cos^4 (х/2)
2(1+cosx)-sin^2x= -(sin^2x-2cosx-2)
-(sin^2x-2cosx-2)=4cos^4(x/2)
cos^2x+2cosx+1=4cos^4(x/2)