Question

cos9xcos7x=cos5xcos3x
x=?​

Answer 1

Answer:

Answer is below

Step-by-step explanation:

2*cos(5x+3x)/2*cos(5x-3x)/2=2*cos(9x+7x)/2*cos(9x-7x)/2  

2*cos4x*cosx=2*cos8x*cosx  

2*cos4x*cosx-2*cos8x*cosx=0  

2*cosx(cos4x-cos8x)=0  

2*cosx(-2*sin(4x+8x)/2*sin(4x-8x)/2)=0  

2*cosx*(2*sin6x*sin2x)=0  

cosx=0 2*sin6x*sin2x=0  

x=пи/2 +пи*n sin6x=0 sin2x=0  

6x=пи*n 2x=пи*n  

x=пи*n/6 x=пи*n/2