Why do we add intervals of pi halves to our solution

The video tutorial explains how to find all solutions for the equation tangent equals ±1. It begins by identifying solutions within the interval 0 to 2π using the unit circle. The instructor then demonstrates how to graph the tangent function to visualize solutions beyond this interval. By understanding the periodic nature of the tangent function, the instructor shows how to extend solutions using π halves increments, avoiding redundancy. The final solution is expressed as X = π/4 + π/2 N, covering all possible solutions.

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