query: To prove $ (\sin x)/x=\cos(x/2)×\cos(x/4)×\cos(x/8)......$
positive_passages.docid: 141787
positive_passages.text: Anybody know a proof of $\prod_{n=1}^\infty\cos(x/2^n)=\sin x/x$.
negative_passages.docid: 76490
negative_passages.text: Proving that $\cos(\arcsin(x))=\sqrt{1-x^2}$
negative_passages.docid: 123920
negative_passages.text: How prove this inequality $\tan{(\sin{x})}>\sin{(\tan{x})}$
negative_passages.docid: 12653
negative_passages.text: Prove $\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$
negative_passages.docid: 85944
negative_passages.text: Prove $ \sin x + \frac{ \sin3x }{3} + ... + \frac{ \sin((2n-1)x) }{2n-1} >0 $
negative_passages.docid: 22058
negative_passages.text: Prove that $\cos(\pi/7)$ is root of equation $8x^3-4x^2-4x+1=0$
negative_passages.docid: 116580
negative_passages.text: Prove by induction: $\sin{x}+\sin{3x}+\dots+\sin{(2n-1)x}=\frac{\sin^2{nx}}{\sin{x}}$
negative_passages.docid: 95085
negative_passages.text: Prove by induction $ \sin x + \sin 2x + ... + \sin nx = \frac {\sin (\frac {n + 1} {2} x)} {\sin \frac{x}{2}} \sin \frac{nx}{2} $
negative_passages.docid: 82758
negative_passages.text: To prove $ \tan(A) + 2 \tan(2A) +4\tan4A + 8 \cot8A =\cot(A) $
negative_passages.docid: 90226
negative_passages.text: Proving trigonometric equation $\cos(36^\circ) - \cos(72^\circ) = 1/2$
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: 35244
negative_passages.text: Prove $\sin^2\theta + \cos^2\theta = 1$
negative_passages.docid: 127380
negative_passages.text: Use vectors to prove $\cos(\beta - \alpha) = \cos \alpha \cos\beta + \sin\alpha \sin\beta$
negative_passages.docid: 59014
negative_passages.text: Prove that $\sin(2A)+\sin(2B)+\sin(2C)=4\sin(A)\sin(B)\sin(C)$ when $A,B,C$ are angles of a triangle
negative_passages.docid: 48586
negative_passages.text: Prove: $\cot x=\sin x\,\sin\left(\frac{\pi}{2}-x\right)+\cos^2x\,\cot x$
negative_passages.docid: 77978
negative_passages.text: Show that $\frac {\sin x} {\cos 3x} + \frac {\sin 3x} {\cos 9x} + \frac {\sin 9x} {\cos 27x} = \frac 12 (\tan 27x - \tan x)$
negative_passages.docid: 105487
negative_passages.text: Prove that $\sin x \cdot \sin (2x) \cdot \sin(3x) < \tfrac{9}{16}$ for all $x$