query: Proof of the identity $\sin(x+y) =\sin(x)\cos(y) + \cos(x)\sin(y)$ for all $x$ and $y$
positive_passages.docid: 147886
positive_passages.text: Proof of the angle sum identity for $\sin$
negative_passages.docid: 55436
negative_passages.text: Why does $A\sin{k(x+c)}=a\sin{kx}+b\cos{kx}$ imply that $A=\sqrt{a^2+b^2}$ and $\tan{c}=-b/a$?
negative_passages.docid: 21941
negative_passages.text: Proving: $x = a_0 + \sum_{n=1}^{\infty}(a_n \cos nx + b_n \sin nx)$
negative_passages.docid: 67172
negative_passages.text: What's the intuition behind the identities $\cos(z)= \cosh(iz)$ and $\sin(z)=-i\sinh(iz)$?
negative_passages.docid: 7712
negative_passages.text: How to prove the both identity (matrix)
negative_passages.docid: 123136
negative_passages.text: Proof of the identity: $c\sin \frac{A-B}{2} \equiv (a-b) \cos \frac{C}{2}$
negative_passages.docid: 143050
negative_passages.text: If $\tan(\frac{\pi}{4}+\frac{y}{2})=\tan^3(\frac{\pi}{4}+\frac{x}{2})$,then prove that $\sin y=\frac{\sin x(3+\sin^2 x)}{(1+3\sin^2 x)}$
negative_passages.docid: 108223
negative_passages.text: If $\cos x=\cos y$ and $\sin x=\sin y$ is $x=y$ or $x=2\pi,y=0$ or $x=0,y=2\pi$? $x,y\in[0,2\pi]$
negative_passages.docid: 52973
negative_passages.text: The identity $(u\times v)\cdot(x\times y)=\begin{vmatrix}u\cdot x&v\cdot x\\ u\cdot y&v\cdot y\\\end{vmatrix}$
negative_passages.docid: 7296
negative_passages.text: Prove $(1-\cos x)/\sin x = \tan x/2$
negative_passages.docid: 65698
negative_passages.text: Proving $\sum\limits_{k=0}^{n}\cos(kx)=\frac{1}{2}+\frac{\sin(\frac{2n+1}{2}x)}{2\sin(x/2)}$
negative_passages.docid: 33905
negative_passages.text: Prove the following trigonometric identity: $\frac{\tan A+\sec A-1}{\tan A-\sec A+1}=\frac{1+\sin A}{\cos A}$
negative_passages.docid: 149447
negative_passages.text: Proving $\sin (x)=\cos (90^\circ-x)$
negative_passages.docid: 120148
negative_passages.text: prove this properties of triangles trigonometric question
negative_passages.docid: 123867
negative_passages.text: Solve $(a + b\sin(x))\sin(x) = p$ for $x$
negative_passages.docid: 73047
negative_passages.text: Proving surjectivity of $\cos(z)$ and $\sin(z)$ and find all $z : \cos(z) \in \mathbb R$ and all $z: \sin(z) \in \mathbb R$
negative_passages.docid: 141645
negative_passages.text: Trigonometric series sum proof