A set of value of x satisfying the equation cos2(12px)+cos2(12qx)=1  form an arithmetic progression with common difference

1+cospx+1+cosqx=2             cos(p+q2)xcos(p−q2)x=0            cos(p+q2)x=0⇒x=(2n+1)πp+q,n=0,±1,±2....  which forms an A.P with common difference2πp+q . and      cos(p−q2)x=0⇒x=(2n+1)πp−q,n=0,±1,±2... which forms an A.P with common difference 2πp−q