Question

Cos10 х *cos 7 х -cos 2 x * cos 15 х =0

Answer 1

Cos10x·cos7x-cos2x·cos15x=0⇒
1/2·[cos(10x-7x)+cos(10x+7x)]-1/2[cos(15x-2x)+cos(15x+2x)]=0
1/2(cos3x+cos17x-cos13x-cos17x)=0
cos3x-cos13x=0⇒
-2sin(3x+13x)/2·sin(3x-13x)/2=0
sin8x·sin(-5x)=0 ⇒ -sin8x·sin5x=0⇒
sin8x=0;    8x=kπ;k∈Z;    x=kπ/8;k∈Z;
sin5x=0;    5x=kπ;k∈Z      x=kπ/5;k∈Z