यहाँ तीन अवस्थाएं सम्भव हैं : 


अब, "n" = "k" + 1 के लिए व्यंजक लिखने पर :

We deduce that the result is true for "n" = "k" + 1 when it is true for "n" = "k". By the principle of mathematical induction it follows that the result is true for all positive integers "n"≥1.

When "n" = 0 the formula is true since formula_7, and (by convention) formula_8.

When "n" < 0, we consider a positive integer "m" such that "n" = −"m". So

Hence, the theorem is true for all integer values of "n".

गणितीय आगमन विधि से सिद्ध
उपयोग
कोज्या (cosine) एवं ज्या (sine) के लिये सूत्र
उपपत्ति (Derivation)