query: How to prove $ \sin^2 {2x} - \sin^2 {x} = \sin {3x}\sin {x} $
positive_passages.docid: 9986
positive_passages.text: Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $
negative_passages.docid: 35244
negative_passages.text: Prove $\sin^2\theta + \cos^2\theta = 1$
negative_passages.docid: 138575
negative_passages.text: Proof that $\cos^2(x)\cosh^2(y) + \sin^2(x)\sinh^2(y) = -1 + \sin^2(x) - \sinh^2(y)$
negative_passages.docid: 48824
negative_passages.text: Prove: $ \frac{1}{\sin 2x} + \frac{1}{\sin 4x } + \cdots + \frac{1 }{\sin 2^n x} = \cot x - \cot 2^n x $
negative_passages.docid: 76490
negative_passages.text: Proving that $\cos(\arcsin(x))=\sqrt{1-x^2}$
negative_passages.docid: 124208
negative_passages.text: Proof $|\sin(x) - x| \le \frac{1}{3.2}|x|^3$
negative_passages.docid: 2251
negative_passages.text: Can someone give me a hint on how to prove this?
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: 44438
negative_passages.text: Prove : $\frac{\cos(x_1) +\cos(x_2) +\cdots+\cos(x_{10})}{\sin(x_1) +\sin(x_2) +\cdots+\sin(x_{10})} \ge 3$
negative_passages.docid: 51979
negative_passages.text: Is there a geometrical method to prove $x<\frac{\sin x +\tan x}{2}$?
negative_passages.docid: 54175
negative_passages.text: Prove the trigonometric identity $\sin^4{x} = \frac{3-4\cos{2x}+\cos{4x}}{8}$
negative_passages.docid: 57330
negative_passages.text: Find the number of solutions of $\sin x+2 \sin 2x- \sin 3x=3$
negative_passages.docid: 53984
negative_passages.text: Prove by induction: $\sum\limits_{k=1}^{n}sin(kx)=\frac{sin(\frac{n+1}{2}x)sin\frac{nx}{2}}{sin\frac{x}{2}}$
negative_passages.docid: 96388
negative_passages.text: Prove $\sin(x)\tan(x) > x^2$ for $x \in ( \,0, \frac{\pi}{2}) \,$
negative_passages.docid: 36366
negative_passages.text: Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$
negative_passages.docid: 141645
negative_passages.text: Trigonometric series sum proof
negative_passages.docid: 54370
negative_passages.text: If $x+y+z=xyz$, prove $\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$