Proving $(\cos x +i\sin x)^n= \cos nx+i\sin nx$ by mathematical induction
10424
Review of a proof for De Moivre's theorem using mathematical induction
60230
Prove that $\frac{1+\sin\theta+i\cos\theta}{1+\sin\theta-i\cos\theta}=\sin\theta+i\cos\theta$
92418
Prove by induction Fibonacci equality
146047
Proving that $\cos(2\pi/n)$ is algebraic
87941
Prove by mathematical induction that $\forall n \in \mathbb{N} : \sum_{k=1}^{2n} \frac{(-1)^{k+1}}{k} = \sum_{k=n+1}^{2n} \frac{1}{k} $
115459
Proving this $F_{n+1} \cdot F_{n-1} - F^2_n = (-1)^n$ by induction
123427
Proving the sum of the first $n$ natural numbers by induction
55869
Use the Maclaurin series to prove that $e^{i\theta} = cos(\theta) + isin(\theta)$
143968
Proving this inequality by mathematical induction
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
139426
Proving $ \binom n 0 ^2 + \binom n 1 ^2 + \dots + \binom n n ^2 = \binom { 2n} n $ without induction
42105
Fibonacci proof by induction
156356
Proof that $x^n+\frac{1}{x^n}\in \mathbb Z$ by complete induction
54175
Prove the trigonometric identity $\sin^4{x} = \frac{3-4\cos{2x}+\cos{4x}}{8}$
149447
Proving $\sin (x)=\cos (90^\circ-x)$
87934
Deducing $\sin x + \cos x \ge 1$ from $(\sin x + \cos x)^2 = 1 + 2 \sin x \cos x$
138683
Proving $\prod_{i=2}^{i=n} \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n}$ by induction