Prove that $\Bbb{R}[\cos(\theta),\sin(\theta)]\cong\Bbb{R}[x,y]/(1-x^2-y^2)$
73445
Is Pythagoras the only relation to hold between $\cos$ and $\sin$?
37985
Show that $|x|^2 = |y|^2$ with $A$ orthogonal and $Ax = \cos (θ)x − \sin (θ)y$, $Ay = \sin (θ)x + \cos (θ) y$
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
34693
Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
24128
How do i show that $w=z^2$ maps $|z-1|\leq 1$ onto $R=2(1+\cos \theta)$?
8554
Proof: $\mathrm{adj}(\mathrm{adj}(A)) = (\mathrm{det}(A))^{n-2} \cdot A$ for $A \in \mathbb{R}^{n\times n}$
8374
How to prove that $R/I \otimes_R M \cong M / IM$
151803
Prove that $R$ is commutative
65319
For all $x,y∈\Bbb{R}$ define that $ x\equiv y$ if$ x^2=y^2$
44119
Prove that $\cos (A + B)\cos (A - B) = {\cos ^2}A - {\sin ^2}B$
101448
Is $\sin^2(z) + \cos^2(z)=1$ still true for $z \in \Bbb{C}$?
281
How one can prove $\prod_{k=1}^{n-1} (\cos\theta-\cos(k\pi/n)) = 2^{1-n}\sin(n\theta)\csc\theta$?
119793
Proving that $D_{12}\cong S_3 \times C_2$
101164
Show that $B \cong \mathbb Z /2\mathbb Z$ for a Boolean field B
118299
Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
136635
Proving that the Fourier Basis is complete for C(R/$2*\pi$ , C) with $L^2$ norm
149447
Proving $\sin (x)=\cos (90^\circ-x)$