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Infinite Series Collection

Infinite Series Collection

I've recently created three questions involving infinite series of trigonometric functions, which can be transformed into a rational function of trig functions, that is

$$\sum_{k=1}^\infty (a_k\sin(k\theta) + b_k\cos(k\theta)) =f(\sin\theta,\;\cos\theta)$$

These questions have recently resurfaced in the further maths A-Level, they also appeared many years ago on the OCR MEI FP2 module, so it was something of a pleasure to remind myself of them!