query: Verifying some trigonometric identities: $\frac{\csc\theta}{\cot\theta}-\frac{\cot\theta}{\csc\theta}=\tan\theta\sin\theta$
positive_passages.docid: 24656
positive_passages.text: Proving that $\frac{\csc\theta}{\cot\theta}-\frac{\cot\theta}{\csc\theta}=\tan\theta\sin\theta$
negative_passages.docid: 111102
negative_passages.text: Prove the Trigonometric Identity: $\frac{\sin x}{1-\cos x} = \frac{1+\cos x}{\sin x}$
negative_passages.docid: 7296
negative_passages.text: Prove $(1-\cos x)/\sin x = \tan x/2$
negative_passages.docid: 81057
negative_passages.text: Evaluation of $\int_{\frac{1}{e}}^{\tan x}\frac{t}{1+t^2}dt+\int_{\frac{1}{e}}^{\cot x}\frac{1}{t(1+t^2)}dt$
negative_passages.docid: 63679
negative_passages.text: Picture/intuitive proof of $\cos(3 \theta) = 4 \cos^3(\theta)-3\cos(\theta)$?
negative_passages.docid: 158807
negative_passages.text: Proving a fact: $\tan(6^{\circ}) \tan(42^{\circ})= \tan(12^{\circ})\tan(24^{\circ})$
negative_passages.docid: 84420
negative_passages.text: When is $\sin(x) = \cos(x)$?
negative_passages.docid: 33396
negative_passages.text: Generalizing a Trig Identity
negative_passages.docid: 42391
negative_passages.text: Calculate $\tan9^{\circ}-\tan27^{\circ}-\tan63^{\circ}+\tan81^{\circ}$
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: 12741
negative_passages.text: How to prove that: $\tan(3\pi/11) + 4\sin(2\pi/11) = \sqrt{11}$
negative_passages.docid: 52413
negative_passages.text: Show that $\tan{(\pi/7)} \tan{(2\pi/7)}\tan{(3\pi/7)}=\sqrt{7}$
negative_passages.docid: 2676
negative_passages.text: Finding $\frac {d(\tan \theta)}{d\theta}$
negative_passages.docid: 40556
negative_passages.text: Why is $\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha$
negative_passages.docid: 98745
negative_passages.text: To prove $(\sin\theta + \csc\theta)^2 + (\cos\theta +\sec\theta)^2 \ge 9$
negative_passages.docid: 11711
negative_passages.text: Prove trigonometry identity for $\cos A+\cos B+\cos C$
negative_passages.docid: 51979
negative_passages.text: Is there a geometrical method to prove $x<\frac{\sin x +\tan x}{2}$?