cos x cos 3x = sin 2x sin 6x

Question

cos x cos 3x = sin 2x sin 6x

Answer 1

cos(x)cos(3x) = sin(2x)sin(6x)

(1.2)*[cos(2x)+cos(4x)]=(1/2)*[cos(4x)-cos(8x)]

cos(2x)+cos(8x)=0

2cos(5x)*cos(3x)=0

a) cos(5x)=0 => 5x=±(pi/2) +pi*n => x=±(pi/10) +pi*n/5

б) cos(3x)=0 => 3x=±(pi/2) +pi*n => x=±(pi/6) +pi*n/3