query: Show that $\tan(A_1+A_2+....A_n) = \frac{s_1-s_3+s_5+...}{1-s_2+s_4-s_6+....}$
positive_passages.docid: 105238
positive_passages.text: Proving $\tan(\theta_1+\theta_2+\cdots+\theta_n)$ has the form $\frac{S_1-S_3+S_5+\cdots}{1-S_2+S_4+\cdots}$
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: 82758
negative_passages.text: To prove $ \tan(A) + 2 \tan(2A) +4\tan4A + 8 \cot8A =\cot(A) $
negative_passages.docid: 123997
negative_passages.text: Finding an expression for $\tan (a+ b + y)$ which involves only $\tan a, \tan b,$ and $\tan y$.
negative_passages.docid: 111847
negative_passages.text: For $a,b,c>0$, prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge a+b+c+\frac{4(a-b)^2}{a+b+c}$
negative_passages.docid: 32197
negative_passages.text: Prove that $\tan A + \tan B + \tan C = \tan A\tan B\tan C,$ $A+B+C = 180^\circ$
negative_passages.docid: 35027
negative_passages.text: Need help with continuing an idea concerning showing that $4\sum\limits_{n \ge 1} a_n^2 \ge \sum\limits_{n \ge 1} \frac1{n^2}(a_1+...+a_n)^2 $
negative_passages.docid: 10289
negative_passages.text: Need help in proving that $\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \frac 1{\sec\theta - \tan\theta}$
negative_passages.docid: 113080
negative_passages.text: Prove $\tan\big(\frac{\pi}{2} -\theta \big) = \cot \theta$
negative_passages.docid: 11059
negative_passages.text: Verify the identity: $\tan^{-1} x +\tan^{-1} (1/x) = \pi /2$
negative_passages.docid: 34275
negative_passages.text: How do I show that $\frac {a^2}b + \frac {b^2}c + \frac {c^2}d + \frac {d^2}a \ge 4$ for $a^2 + b^2 + c^2 + d^2 = 4$?
negative_passages.docid: 79685
negative_passages.text: For natural $n$, prove $\prod_{k=1}^n \tan\left(\frac{k\pi}{2n+1}\right) = 2^n \prod_{k=1}^n \sin\left(\frac{k\pi}{2n+1}\right)=\sqrt{2n+1}$
negative_passages.docid: 124248
negative_passages.text: $1+\frac {1}{4}(1+\frac {1}{4}) +\frac {1}{9}(1+\frac {1}{4} +\frac {1}{9})+....$
negative_passages.docid: 105117
negative_passages.text: $1 + \frac{1}{3}\frac{1}{4} + \frac{1}{5}\frac{1}{4^2} + \frac{1}{7}\frac{1}{4^3} + ..........$
negative_passages.docid: 8919
negative_passages.text: If $\alpha = \frac{2\pi}{7}$ then the find the value of $\tan\alpha .\tan2\alpha +\tan2\alpha \tan4\alpha +\tan4\alpha \tan\alpha.$
negative_passages.docid: 9539
negative_passages.text: $\alpha$ and $\beta$ are solution of $a \cdot \tan\theta + b \cdot \sec\theta = c$ show $ \tan(\alpha + \beta) = \frac{2ac}{a^2 - c^2}$
negative_passages.docid: 50777
negative_passages.text: Prove that $4\sin\frac{2\pi}{7}- \tan\frac{\pi}{7}= \sqrt{7}$ .