User Sooraj S

9 votes

Computing the integral of $\log(\sin x)$

answered Jun 1, 2018 at 19:53

6 votes

How was the normal distribution derived?

answered Apr 21, 2020 at 18:50

5 votes

Derivation of Mode of grouped data

answered May 24, 2020 at 22:40

5 votes

Proofs of AM-GM inequality

answered Feb 20, 2018 at 9:58

5 votes

Determine the number of equivalence relations on the set {1, 2, 3, 4}

answered Jan 2, 2018 at 17:08

5 votes

The median minimizes the sum of absolute deviations (the $ {\ell}_{1} $ norm)

answered Jul 20, 2017 at 11:32

5 votes

Proof for the formula of sum of arcsine functions $ \arcsin x + \arcsin y $

answered Dec 6, 2018 at 4:43

4 votes

How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)

answered Dec 26, 2017 at 19:21

4 votes

Stirling numbers combinatorial proof

answered Jan 15, 2018 at 21:20

4 votes

Accepted

Equate $e^{-i|Ψ⟩⟨Ψ|Δt}e^{-i|x⟩⟨x|Δt}$ to $(\cos^2Δt/2-\sin^2Δt/2ψ.z)I\\-2i\sinΔt/2[\cosΔt/2\frac{ψ+z}{2}+\sinΔt/2\frac{ψ\times z}{2}].\vec{σ}$

answered Jul 28, 2022 at 16:54

3 votes

Stirling's formula: proof?

answered Feb 21, 2021 at 3:40

3 votes

Accepted

Derive the conditions $xy<1$ for $\tan^{-1}x+\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy}$ and $xy>-1$ for $\tan^{-1}x-\tan^{-1}y=\tan^{-1}\frac{x-y}{1+xy}$

answered Jan 14, 2018 at 17:23

2 votes

Accepted

Evaluate $\int_0^\pi\frac{\sin\left(n+\frac{1}{2}\right)x}{\sin \frac{x}{2}}dx$

answered Jan 15, 2020 at 23:01

2 votes

Accepted

Filippov's Inductive proof for Jordan Canonical form

answered Nov 17, 2020 at 15:10

2 votes

Accepted

Prove $e^{(A+B)\Delta t}=e^{A\Delta t}e^{B\Delta t}e^{-1/2[A,B]\Delta t^2}+O(\Delta t^3)$

answered Oct 30, 2021 at 13:34

1 vote

Accepted

Derive the step deviation method for mean

answered May 27, 2020 at 17:21

1 vote

Accepted

Linear independence of vectors and minor of matrices

answered Jul 14, 2020 at 22:18

1 vote

Accepted

Discrete Logarithm Problem as Period finding of a function

answered Jun 12, 2022 at 18:58

1 vote

Accepted

Equation of a hyperbola given its asymptotes

answered Nov 8, 2019 at 6:18

1 vote

Accepted

If $x\sqrt{1+y}+y\sqrt{1+x}=0$ find $y'$

answered Apr 8, 2018 at 6:55

1 vote

Accepted

Maximum/Minimum of $f(x)=\sin(2x)+5$ using second derivative test

answered Apr 27, 2018 at 19:10

1 vote

Accepted

Solve $\dfrac{dy}{dx}=\cos(x+y)+\sin(x+y)$

answered Jun 18, 2018 at 18:03

1 vote

Simplest way to integrate $\int \frac{1}{1+\tan x}dx,$

answered May 29, 2018 at 17:03

1 vote

If $A,B>0$ and $A+B = \frac{\pi}{3},$ Then find Maximum value of $\tan A\cdot \tan B$.

answered Oct 17, 2018 at 8:37

1 vote

Why does partial differentiation of a pair of straight lines give the point of intersection of those straight lines?

answered Oct 18, 2019 at 19:42

1 vote

Trigonometric function integration: $\int_0^{\pi/2}\frac{dx}{(a^2\cos^2x+b^2 \sin^2x)^2}$

answered May 28, 2018 at 21:56

1 vote

Inverse of a Function exists iff Function is bijective

answered Jan 9, 2018 at 13:46

1 vote

Accepted

Proof of the Associative property of the Least common multiple

answered Dec 31, 2017 at 14:19

1 vote

Show injectivity of the composition of two injective functions

answered Jan 5, 2018 at 22:34

1 vote

Accepted

Prove $\exp{i\frac{\pi}{2}(-1+\sigma_{i})}=\sigma_{i}$

answered Dec 31, 2015 at 9:31

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57 Answers

Computing the integral of $\log(\sin x)$

How was the normal distribution derived?

Derivation of Mode of grouped data

Proofs of AM-GM inequality

Determine the number of equivalence relations on the set {1, 2, 3, 4}

The median minimizes the sum of absolute deviations (the $ {\ell}_{1} $ norm)

Proof for the formula of sum of arcsine functions $ \arcsin x + \arcsin y $

How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)

Stirling numbers combinatorial proof

Equate $e^{-i|Ψ⟩⟨Ψ|Δt}e^{-i|x⟩⟨x|Δt}$ to $(\cos^2Δt/2-\sin^2Δt/2ψ.z)I\\-2i\sinΔt/2[\cosΔt/2\frac{ψ+z}{2}+\sinΔt/2\frac{ψ\times z}{2}].\vec{σ}$

Stirling's formula: proof?

Derive the conditions $xy<1$ for $\tan^{-1}x+\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy}$ and $xy>-1$ for $\tan^{-1}x-\tan^{-1}y=\tan^{-1}\frac{x-y}{1+xy}$

Evaluate $\int_0^\pi\frac{\sin\left(n+\frac{1}{2}\right)x}{\sin \frac{x}{2}}dx$

Filippov's Inductive proof for Jordan Canonical form

Prove $e^{(A+B)\Delta t}=e^{A\Delta t}e^{B\Delta t}e^{-1/2[A,B]\Delta t^2}+O(\Delta t^3)$

Derive the step deviation method for mean

Linear independence of vectors and minor of matrices

Discrete Logarithm Problem as Period finding of a function

Equation of a hyperbola given its asymptotes

If $x\sqrt{1+y}+y\sqrt{1+x}=0$ find $y'$

Maximum/Minimum of $f(x)=\sin(2x)+5$ using second derivative test

Solve $\dfrac{dy}{dx}=\cos(x+y)+\sin(x+y)$

Simplest way to integrate $\int \frac{1}{1+\tan x}dx,$

If $A,B>0$ and $A+B = \frac{\pi}{3},$ Then find Maximum value of $\tan A\cdot \tan B$.

Why does partial differentiation of a pair of straight lines give the point of intersection of those straight lines?

Trigonometric function integration: $\int_0^{\pi/2}\frac{dx}{(a^2\cos^2x+b^2 \sin^2x)^2}$

Inverse of a Function exists iff Function is bijective

Proof of the Associative property of the Least common multiple

Show injectivity of the composition of two injective functions

Prove $\exp{i\frac{\pi}{2}(-1+\sigma_{i})}=\sigma_{i}$