query: Is $\sin^2 x $ the same as $\sin x^2$?
positive_passages.docid: 156162
positive_passages.text: Are $\cos^2 \theta$ and $\cos \theta^2$ the same?
negative_passages.docid: 96436
negative_passages.text: About integrating $\sin^2 x$ by parts
negative_passages.docid: 31379
negative_passages.text: Relationship between $\tanh x$ and $\arctan x$
negative_passages.docid: 30953
negative_passages.text: Is $\sum_{k=1}^{n} \sin(k^2)$ bounded by a constant $M$?
negative_passages.docid: 87242
negative_passages.text: Ways to prove $ \int_0^\pi dx \frac{\sin^2(n x)}{\sin^2 x} = n\pi$
negative_passages.docid: 140936
negative_passages.text: If two integrals are equal, then the functions are the same
negative_passages.docid: 17707
negative_passages.text: Why is ${x^{\frac{1}{2}}}$ the same as $\sqrt x $?
negative_passages.docid: 60261
negative_passages.text: Is $\sqrt{x^2}=|x|$ or $=x$? Isn't $(x^2)^\frac12=x?$
negative_passages.docid: 82630
negative_passages.text: How is it, that $\sqrt{x^2}$ is not $ x$, but $|x|$?
negative_passages.docid: 102777
negative_passages.text: Is $G^{(X, Y)} = (G^X)^Y?$ ($A^B$ just means that $B$ is mapped to $A$)
negative_passages.docid: 113168
negative_passages.text: If $a > b$, is $a^2 > b^2$?
negative_passages.docid: 44119
negative_passages.text: Prove that $\cos (A + B)\cos (A - B) = {\cos ^2}A - {\sin ^2}B$
negative_passages.docid: 41447
negative_passages.text: tough integral involving $\sin(x^2)$ and $\sinh^2 (x)$
negative_passages.docid: 55175
negative_passages.text: Is the function $f(x) = x^2 - 2x$ one-to-one?
negative_passages.docid: 60559
negative_passages.text: How prove this $x^3<\sin^2{x}\tan{x},x\in\left(0,\dfrac{\pi}{2}\right)$
negative_passages.docid: 102138
negative_passages.text: Why does $\sqrt{x^2}$ seem to equal $x$ and not $|x|$ when you multiply the exponents?
negative_passages.docid: 58901
negative_passages.text: Why is every such function constant: $f(x)=f(x^2)$ for $x \in [0,1]$?