Question

cos5x+cos7x=cos(п+6x)

Answer 1

cos 5x+cos 7x=cos(П+6x)

2cos6x*cosx=-cos6x

2cos6x*cosx+cos6x=0

cos6x(2сosx+1)=0

cos6x=0        или      2cosx=1=0

6x=П/2+Пk, kєZ         cosx=-1/2

x=П/12+Пk/6, kєZ       x=+-2П/3+2Пk, kєZ

Answer 2

cos5x+cos7x=cos(pi+6x)

2cos12x/2 *cos2x/2=-cos6x

2cos6x*cosx+cos6x=0

cos6x(2cosx+1)=0

cos6x=0  или            2cosx+1=0

6х=pi/2+pi*n            cosx=-1/2

x=pi*n/12+pi*n/6      x=+-2pi/3+2pi*k