cos5x+cos7x=cos(П+6х)

cos5x+cos7x=cos(π+6x)  так как cos(α+π)=-cos(α) тоcos5x+cos7x=-cos6xcos5x+cos6x+cos7x=0так как cosα+cosβ=2cos(α+β)/2 *cos(α-β)/2 то получаем(cos7x+cos5x)+cos6x=02cos((5+7)/2)*cos((7-5)/2)+cos6x=02cos6x*cosx+cos6x=0cos6x(2cosx+1)=0cos6x=06x=π/2+πn  n=0,1,2,3․․․․x=π/12+πn  n=0,1,2,3․․․․или 2cosx+1=0cosx=-1/2x=2π/3+2πn  n=0,1,2,3․․․․x=4π/3+2πn  n=0,1,2,3․․․․ответы так жеx=π/12+πn  n=0,1,2,3․․․․x=2π/3+2πn  n=0,1,2,3․․․․x=4π/3+2πn  n=0,1,2,3․․․․