query: Prove that: $\sec^2 20^\circ +\sec^2 40^\circ +\sec^2 80^\circ = \textrm 36$
positive_passages.docid: 142673
positive_passages.text: Evaluate $\tan^{2}(20^{\circ}) + \tan^{2}(40^{\circ}) + \tan^{2}(80^{\circ})$
negative_passages.docid: 50266
negative_passages.text: In the following figure prove that: $AK||BC$
negative_passages.docid: 50226
negative_passages.text: Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$
negative_passages.docid: 148094
negative_passages.text: Show that $e^3 > 20$
negative_passages.docid: 149801
negative_passages.text: prove that $TS = ST$
negative_passages.docid: 46106
negative_passages.text: Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
negative_passages.docid: 148744
negative_passages.text: Prove that $(\frac{bc+ac+ab}{a+b+c})^{a+b+c} \ge \sqrt{(bc)^a(ac)^b(ab)^c}$
negative_passages.docid: 54512
negative_passages.text: How do I prove: $\cos (\theta + 90^\circ) \equiv - \sin \theta $
negative_passages.docid: 108916
negative_passages.text: On the proof $\tan 70°-\tan 20° -2 \tan 40°=4\tan 10°$
negative_passages.docid: 55984
negative_passages.text: How can I find the answer to $\varphi(2^{400} + 2)$?
negative_passages.docid: 114411
negative_passages.text: Simple Proof of the Euler Identity $\exp{i\theta}=\cos{\theta}+i\sin{\theta}$
negative_passages.docid: 35167
negative_passages.text: Prove congruence using fermat's thm
negative_passages.docid: 69673
negative_passages.text: Prove that $\left (\frac{a^2 + b^2 +c^2}{a+b+c} \right) ^ {(a+b+c)} > a^a b^b c^c$
negative_passages.docid: 152167
negative_passages.text: Prove that if $x,y,z$ are integers such that $x^2+y^2=z^2$, then $xyz \equiv o \pmod{60}$.
negative_passages.docid: 139426
negative_passages.text: Proving $ \binom n 0 ^2 + \binom n 1 ^2 + \dots + \binom n n ^2 = \binom { 2n} n $ without induction
negative_passages.docid: 120795
negative_passages.text: Showing that $\sin^2x\cdot\sin^22x\cdot\sin^24x\cdot\sin^28x\cdots\sin^22^nx\leq\frac{3^n}{4^n}$
negative_passages.docid: 41141
negative_passages.text: Proving that $\frac{\phi^{400}+1}{\phi^{200}}$ is an integer.