# All Questions

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### Points of contacts of tangents of the curve $y=\sin x$

Prove that the points of contacts of tangents of the curve $y=\sin x$ drawn from origin lie on the curve $1/x^2 -1/y^2 = -1$
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### Prove that there is no continuous function $f : \Bbb R → \Bbb R$ such that $f = χ_I$ almost everywhere on $\Bbb R$.

Let $I = [0,1]$ and $χ_I : \Bbb R → \Bbb R$ be the characteristic function on $I$. Prove that there is no continuous function $f : \Bbb R → \Bbb R$ such that $f = χ_I$ almost everywhere on $\Bbb R$. ...
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### Proving a compact Lie group admits a biinvariant metric

At the end of a lesson in Differential Geometry, my teacher said: Fatto, che non dimostriamo, non è difficile ma il tempo scarseggia, se $G$ è compatto possiamo sempre trovare una metrica ...
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### Let $A$ be a real symmetric matrix with rank $1$ , then can all the diagonal entries of $A$ be $0$ ?

Let $A$ be a square real symmetric matrix with rank $1$ , then can all the diagonal entries of $A$ be $0$ ? I know that real symmetric matrices are diagonalizable . Also if all the diagonal entries be ...
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