InterviewSolution
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InterviewSolution
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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)`. |
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Answer» `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)` |
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