Prove $\left|\begin{smallmatrix} \sin^2x&\cot x&1\\ \sin^2y&\cot y&1\\ \sin^2z&\cot z&1 \end{smallmatrix}\right|=0$ if $x+y+z=\pi$
101476
If $A$, $B$ and $C$ are the angles of a triangle then find the value of $\Delta$
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
24656
Proving that $\frac{\csc\theta}{\cot\theta}-\frac{\cot\theta}{\csc\theta}=\tan\theta\sin\theta$
36639
Prove by induction that $\sum_{r=0}^{n}\begin{pmatrix}n \\ r \end{pmatrix}=2^k$
140459
Why is $\left(e^{2\pi i}\right)^i \neq e^{-2 \pi}$?
44438
Prove : $\frac{\cos(x_1) +\cos(x_2) +\cdots+\cos(x_{10})}{\sin(x_1) +\sin(x_2) +\cdots+\sin(x_{10})} \ge 3$
120867
How prove this two symmetric matrices $AB=0$
34017
Show that $n^{\pi\left(2n\right)-\pi\left(n\right)}2$
54512
How do I prove: $\cos (\theta + 90^\circ) \equiv - \sin \theta $
69673
Prove that $\left (\frac{a^2 + b^2 +c^2}{a+b+c} \right) ^ {(a+b+c)} > a^a b^b c^c$
94962
For complex $z$, $|z| = 1 \implies \text{Re}\left(\frac{1-z}{1+z}\right)  = 0$
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
45171
How prove this $(p-1)!\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{p-1}\right)\equiv 0\pmod{p^2}$
97011
Proving that $\prod_{k=1}^{n}\tan\left(\frac{\pi k}{2n+1}\right)=\sqrt{2n+1}$ using geometry
35244
Prove $\sin^2\theta + \cos^2\theta = 1$
116223
Show that the angles satisfy $x+y=z$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$