query: Geometric Proof that $\frac{d}{d\theta}(\tan{\theta}) = 1 + \tan^{2}{\theta}$
positive_passages.docid: 2676
positive_passages.text: Finding $\frac {d(\tan \theta)}{d\theta}$
negative_passages.docid: 65809
negative_passages.text: Show that $d_2$ defined by $d_2(x,y)=\frac{|x-y|}{1+|x-y|}$ is a metric
negative_passages.docid: 142835
negative_passages.text: Proving :$\arctan(1)+\arctan(2)+ \arctan(3)=\pi$
negative_passages.docid: 97011
negative_passages.text: Proving that $\prod_{k=1}^{n}\tan\left(\frac{\pi k}{2n+1}\right)=\sqrt{2n+1}$ using geometry
negative_passages.docid: 111601
negative_passages.text: Evaluating $\int \tan^{1/3}(\theta) d \theta$
negative_passages.docid: 21855
negative_passages.text: Prove $\sum_{n=1}^{\infty}\arctan{\left(\frac{1}{n^2+1}\right)}=\arctan{\left(\tan\left(\pi\sqrt{\frac{\sqrt{2}-1}{2}}\right)\cdots\right)}$
negative_passages.docid: 145632
negative_passages.text: Proving $\frac{1}{\cos^2\alpha}<\frac{\tan\beta-\tan\alpha}{\beta-\alpha}<\frac{1}{\cos^2\beta}$
negative_passages.docid: 141643
negative_passages.text: Showing $\rho (x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric
negative_passages.docid: 70765
negative_passages.text: If $\frac{\tan(a+b-c)}{\tan(a-b+c)}=\frac{\tan c}{\tan b}$, then $\sin(b-c)=0$ or $\sin 2a + \sin2b + \sin 2c=0$
negative_passages.docid: 147648
negative_passages.text: Proving $\frac{a}{a^2-a+1}+\frac{b}{b^2-b+1}+\frac{c}{c^2-c+1}+\frac{d}{d^2-d+1}\le \frac{8}{3}$ given $a+b+c+d=2$
negative_passages.docid: 46353
negative_passages.text: Proof that $\cos(\pi/3)=1/2$
negative_passages.docid: 60559
negative_passages.text: How prove this $x^3<\sin^2{x}\tan{x},x\in\left(0,\dfrac{\pi}{2}\right)$
negative_passages.docid: 96388
negative_passages.text: Prove $\sin(x)\tan(x) > x^2$ for $x \in ( \,0, \frac{\pi}{2}) \,$
negative_passages.docid: 26790
negative_passages.text: Proving the geometric sum formula by induction
negative_passages.docid: 105707
negative_passages.text: A proof of $\int_{0}^{1}\left( \frac{\ln t}{1-t}\right)^2\,\mathrm{d}t=\frac{\pi^2}{3}$
negative_passages.docid: 129605
negative_passages.text: $ 2g(z)=g(\frac{z}{2}) + g(\frac{z+1}{2})$
negative_passages.docid: 48586
negative_passages.text: Prove: $\cot x=\sin x\,\sin\left(\frac{\pi}{2}-x\right)+\cos^2x\,\cot x$