If `cos p theta+cos q theta=0`, then prove that the different values of `theta` are in A.P. with common difference `2pi// (p pm q)`.

Explanation

`cos p theta = - cos q theta = cos (pi - q theta)`
`rArr p theta = 2 n pi -+ (pi - q theta)`
`rArr (p -+ q) theta = (2n -+ 1) pi`
`rArr theta = ((2n -+1)pi)/((p pm q)), n in Z`
`rArr theta = (r pi)/(p -+ q), " where " r = -3, -1, 1, 3`....
`rArr theta = ...., (-3pi)/(p-+q) , (-pi)/(p-+q), (pi)/(p-+q), (3pi)/(p-+q)`,....
The above series is an A.P., of common difference `= (2pi)/(p -+q)`