query: If $\sin \theta+\cos\theta+\tan\theta+\cot\theta+\sec\theta+\csc\theta=7$, then $\sin 2\theta$ is a root of $x^2 -44x +36=0$ My own bonafide attempt.
positive_passages.docid: 143070
positive_passages.text: If $\sin A + \cos A + \tan A + \cot A + \sec A + \csc A = 7$ then $x^2 - 44x - 36 = 0$ holds for $x=\sin 2A$
negative_passages.docid: 100907
negative_passages.text: $\sin\alpha + \sin\beta + \sin\gamma = 4\cos{\frac{\alpha}{2}}\cos{\frac{\beta}{2}}\cos{\frac{\gamma}{2}}$ when $\alpha + \beta + \gamma = \pi$
negative_passages.docid: 48956
negative_passages.text: Simplify $\arctan (\frac{1}{2}\tan (2A)) + \arctan (\cot (A)) + \arctan (\cot ^{3}(A)) $
negative_passages.docid: 22058
negative_passages.text: Prove that $\cos(\pi/7)$ is root of equation $8x^3-4x^2-4x+1=0$
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: 145463
negative_passages.text: How to factorise $2 \sin^2θ – 3\sinθ +1 = 0$
negative_passages.docid: 35244
negative_passages.text: Prove $\sin^2\theta + \cos^2\theta = 1$
negative_passages.docid: 108223
negative_passages.text: If $\cos x=\cos y$ and $\sin x=\sin y$ is $x=y$ or $x=2\pi,y=0$ or $x=0,y=2\pi$? $x,y\in[0,2\pi]$
negative_passages.docid: 143050
negative_passages.text: If $\tan(\frac{\pi}{4}+\frac{y}{2})=\tan^3(\frac{\pi}{4}+\frac{x}{2})$,then prove that $\sin y=\frac{\sin x(3+\sin^2 x)}{(1+3\sin^2 x)}$
negative_passages.docid: 150300
negative_passages.text: Root of unity for $n+1$
negative_passages.docid: 95633
negative_passages.text: Help with this trigonometry problem
negative_passages.docid: 63679
negative_passages.text: Picture/intuitive proof of $\cos(3 \theta) = 4 \cos^3(\theta)-3\cos(\theta)$?
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: 84420
negative_passages.text: When is $\sin(x) = \cos(x)$?
negative_passages.docid: 108808
negative_passages.text: $x =r\cos \theta$ and $y = r\sin\theta$, determine $\frac{\partial r}{\partial x}$ and $\frac{\partial \theta}{\partial x}$
negative_passages.docid: 24656
negative_passages.text: Proving that $\frac{\csc\theta}{\cot\theta}-\frac{\cot\theta}{\csc\theta}=\tan\theta\sin\theta$
negative_passages.docid: 148535
negative_passages.text: Finding the "triangular root" of a number.