Derivation of $\cos^2z+\sin^2z=1$
742
How to prove Euler's formula: $e^{i\varphi}=\cos(\varphi) +i\sin(\varphi)$?
44438
Prove : $\frac{\cos(x_1) +\cos(x_2) +\cdots+\cos(x_{10})}{\sin(x_1) +\sin(x_2) +\cdots+\sin(x_{10})} \ge 3$
116580
Prove by induction: $\sin{x}+\sin{3x}+\dots+\sin{(2n-1)x}=\frac{\sin^2{nx}}{\sin{x}}$
45343
Solve $\cos^{n}x-\sin^{n}x=1$ with $n\in \mathbb{N}$.
67172
What's the intuition behind the identities $\cos(z)= \cosh(iz)$ and $\sin(z)=-i\sinh(iz)$?
90226
Proving trigonometric equation $\cos(36^\circ) - \cos(72^\circ) = 1/2$
9986
Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $
69020
Complex analysis : If $z =re^{i\theta}$, then prove that $|e^{iz}| =e^{-r\sin\theta}$
36457
Closed form for $\int \frac{1}{\sin^nx +\cos^mx}dx$
39492
Finding $z\in \mathbb C$ with $\sin z = 2$?
30723
Second derivative "formula derivation"
57750
Solve identity: $\frac {\sin x}{1-\cos x} = \frac {1+\cos x}{\sin x}$
14386
Proof of an equality involving cosine $\sqrt{2 + \sqrt{2 + \cdots + \sqrt{2 + \sqrt{2}}}}\ =\ 2\cos (\pi/2^{n+1})$
100320
Prove that $\cos\frac {2\pi}{7}+ \cos\frac {4\pi}{7}+ \cos\frac {8\pi}{7}=-\frac{1}{2}$
24656
Proving that $\frac{\csc\theta}{\cot\theta}-\frac{\cot\theta}{\csc\theta}=\tan\theta\sin\theta$
141645
Trigonometric series sum proof
17769
Show that $\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x} = \frac{1}{2}\left(\tan 27x-\tan x\right)$