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Many applications require to determine thek-nearest neighbors for multiple query points simultaneously. This task is known as all-(k)-nearest-neighbor (AkNN) query. In this paper, we suggest a new method for efficient AkNN query processing which is based on spherical approximations for indexing and query set representation. In this setting, we propose trigonometric pruning which enables a significant decrease of the remaining search space for a query. Employing this new pruning method, we considerably speed up AkNN queries.