query: Trigonometric Identity: $2\cos{A}\sin{B}\sin{C} = \sin^2{B} + \sin^2{C} - \sin^2{A}$ in the case $A + B + C = \pi$
positive_passages.docid: 16270
positive_passages.text: Trigonometry question: $\sin^2(A) + \sin^2(B) - \sin^2(C) = 2\sin(A)\sin(B)\cos(C).$
negative_passages.docid: 81102
negative_passages.text: Cosine of the sum of two solutions of trigonometric equation $a\cos \theta + b\sin \theta = c$
negative_passages.docid: 48586
negative_passages.text: Prove: $\cot x=\sin x\,\sin\left(\frac{\pi}{2}-x\right)+\cos^2x\,\cot x$
negative_passages.docid: 9986
negative_passages.text: Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $
negative_passages.docid: 40556
negative_passages.text: Why is $\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha$
negative_passages.docid: 87934
negative_passages.text: Deducing $\sin x + \cos x \ge 1$ from $(\sin x + \cos x)^2 = 1 + 2 \sin x \cos x$
negative_passages.docid: 56195
negative_passages.text: Find the minimum value of $\sin^{2} \theta +\cos^{2} \theta+\sec^{2} \theta+\csc^{2} \theta+\tan^{2} \theta+\cot^{2} \theta$
negative_passages.docid: 57750
negative_passages.text: Solve identity: $\frac {\sin x}{1-\cos x} = \frac {1+\cos x}{\sin x}$
negative_passages.docid: 137376
negative_passages.text: Proving a trig identity: $\frac{\sin(A + B)}{\sin(A - B)}=\frac{\tan A + \tan B}{\tan A - \tan B}$
negative_passages.docid: 48881
negative_passages.text: Verification the integral identity $\int_0^\pi \ln(1+\alpha\cos(x))dx=\pi\ln\left(\frac{1+\sqrt{1-\alpha^2}}{2}\right)$.
negative_passages.docid: 115743
negative_passages.text: In Triangle, $\sin\frac A2\!+\!\sin\frac B2\!+\!\sin\frac C2\!-\!1\!=\!4\sin\frac{\pi -A}4\sin\frac{\pi -B}4\sin\frac{\pi-C}4$
negative_passages.docid: 56059
negative_passages.text: If $\frac{\sin^4 x}{a}+\frac{\cos^4 x}{b}=\frac{1}{a+b}$, then show that $\frac{\sin^6 x}{a^2}+\frac{\cos^6 x}{b^2}=\frac{1}{(a+b)^2}$
negative_passages.docid: 102320
negative_passages.text: Is my solution correct for solving $\cos(z)=2$, $z\in \mathbb{C}$
negative_passages.docid: 42545
negative_passages.text: If $ a,b,c\in \left(0,\frac{\pi}{2}\right)\;,$ Then prove that $\frac{\sin (a+b+c)}{\sin a+\sin b+\sin c}<1$
negative_passages.docid: 86454
negative_passages.text: How to prove $\cos\left(\pi\over7\right)-\cos\left({2\pi}\over7\right)+\cos\left({3\pi}\over7\right)=\cos\left({\pi}\over3 \right)$
negative_passages.docid: 65503
negative_passages.text: Identity involving LCM and GCD: $\frac{[a,b,c]^2}{[a,b][b,c][c,a]}=\frac{(a,b,c)^2}{(a,b)(b,c)(c,a)}$
negative_passages.docid: 27628
negative_passages.text: Solving $a \sin\theta + b \cos\theta = c$