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1h
comment Difficult inverse tangent identity
Its not given equality, but a proposition to be verified. If you take $\theta=\arcsin(x)$ by the definition of Principal value,$$-\dfrac\pi2\le x\le\dfrac\pi2\implies\cos\theta\ge0$$ and consequently $$|\cos\theta|=+\cos\theta$$
2h
comment Difficult inverse tangent identity
For the sake of completeness, you should explain why $$\sqrt{1-\sin^2\theta}=|\cos\theta|$$ reduces to $$+\cos\theta$$
2h
answered Difficult inverse tangent identity
3h
comment reflection of the point $(1,0)$
@Mathxx, Please find the edited version
3h
revised reflection of the point $(1,0)$
added 1 character in body
3h
comment For which $n$ does $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$ imply $\frac{1}{a^n}+\frac{1}{b^n}+\frac{1}{c^n}=\frac{1}{a^n+b^n+c^n}$
@LinusS. The derivation is even easier & natural if we write $$\dfrac1a+\dfrac1b=\dfrac1{a+b+c}-\dfrac1c$$ to get $$(a+b)(c^2+bc+ca+ab)=0$$ and $$c^2+bc+ca+ab=(c+a)(c+b)$$
3h
answered reflection of the point $(1,0)$
8h
revised Difficult inverse tangent identity
added 369 characters in body
8h
answered Difficult inverse tangent identity
19h
comment Find an acute angle $\gamma$ such that $\sin \gamma + \cos \gamma= \sqrt{2}$
See en.wikibooks.org/wiki/Trigonometry/… or en.wikipedia.org/wiki/Tangent_half-angle_substitution
19h
comment Find the greatest positive integer $x$ such that $23^{6+x}$ divides $2000!$
possible duplicate of Highest power of a prime $p$ dividing $N!$
20h
comment Finding extreme values of a variable on an intersection of a sphere and a plane
@Lozansky, en.wikipedia.org/wiki/Lagrange_multiplier $f_x$ is the first order partial derivative wrt $x$
20h
comment Finding extreme values of a variable on an intersection of a sphere and a plane
@Lozansky, Using Lagrange multipliers $$f(x,y,z)=z+a(x^2+y^2+z^2-1)+b(x+2y+2z)$$ Then find $f_x,f_y,f_z$
21h
comment Solving $7[x]+23\{x\}=191$
@Integrator, Nice to see your response
21h
comment Is it possible to have $a^2 + b^2 = c^2 + 1$ for $a$, $b$, $c$ being coprime integers?
Wish I know the mistake here. One can easily check with example like $$a=26,b=21\implies d=4,c=5$$
21h
comment Finding extreme values of a variable on an intersection of a sphere and a plane
@Lozansky, Arranged it as a Quadratic Equation in $y$
21h
revised Is it possible to have $a^2 + b^2 = c^2 + 1$ for $a$, $b$, $c$ being coprime integers?
added 173 characters in body
21h
answered Is it possible to have $a^2 + b^2 = c^2 + 1$ for $a$, $b$, $c$ being coprime integers?
22h
comment The maclaurin series $ f(x) =\frac {x^3} {2+ x^2}$
$$=x^3/2\left(1+x^2/2\right)^{-1}$$
22h
answered $a^2 + b^2$ never leaves remainder $3$ when divided by $4$