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Apr
20
comment Differentiating the function $\arcsin(3x-4x^3)$
If $x>1/2, \arcsin(3x-4x^3)=-(3\arcsin x-\pi)$ and for $x<-1/2, \arcsin(3x-4x^3)=-\pi-3\arcsin x$
Apr
20
comment Simplify $(x_1+x_2+\dots+x_m)^p$?
mathworld.wolfram.com/MultinomialTheorem.html
Apr
19
comment $\cot^{-1}(x)=\pi+\tan^{-1}(1/x)$ when $x<0$
See math.stackexchange.com/questions/304399/… and math.stackexchange.com/questions/610261/…
Apr
19
comment Is $a \sin x + b \sin y \leq \sin(ax + by)$ true?
See math.stackexchange.com/questions/128888/…
Apr
19
comment Simplify $ \csc(65^{\circ} + \theta) - \sec(25^{\circ} - \theta) - \tan(55^{\circ} - \theta) + \cot(35^{\circ} + \theta) $.
@Abhishekstudent, See proofwiki.org/wiki/…
Apr
19
comment Simplify $ \csc(65^{\circ} + \theta) - \sec(25^{\circ} - \theta) - \tan(55^{\circ} - \theta) + \cot(35^{\circ} + \theta) $.
@Abhishekstudentm $$65^\circ+\theta+(25^\circ-\theta)=90^\circ\iff65^\circ+\theta=90^\circ-(25 ^\circ-\theta)$$
Apr
19
comment limit evaluation calculus I
See math.stackexchange.com/questions/1205475/…
Apr
19
comment Proving a complicated identity
@Unknown,In case you don't know Double Angle Formula, see the alternative method
Apr
18
comment Proving a complicated identity
@ClaudeLeibovici, Thanks. I'm an Introvert:)
Apr
18
comment How to find the maximum and minimum of the function $f(x) = \frac{3x}{x^2 -2x + 4}$
Related : math.stackexchange.com/questions/174905/…
Apr
18
comment Solve $x + y + z = xyz$ such that $x , y , z \neq0$
math.stackexchange.com/questions/613105/…
Apr
18
comment A theoretic question about cosine general solution.
@Meitar, For $\cos x/2=-1/\sqrt2,=-\cos\pi/4=\cos(\pi-\pi/4)\implies x/2=2m\pi\pm(\pi-\pi/4)$
Apr
18
comment A theoretic question about cosine general solution.
@Meitar, Whenever, you've reached $$\cos^2\dfrac x2=\dfrac12,$$ you use $\cos2y$ formula. Similarly for $\sin^2,\tan^2$
Apr
18
comment Number Theory - Multiple of $36$ problem
artofproblemsolving.com/wiki/index.php/2010_AIME_II_Problems and artofproblemsolving.com/community/…
Apr
18
comment How to solve this complex logarithm equation?
@VitoChou, $$\dfrac ab=\dfrac cd=\pm\sqrt{\dfrac{a^2-c^2}{b^2-d^2}}$$
Apr
17
comment How to solve this complex logarithm equation?
Wish I know the mistake here
Apr
17
comment the derivative of $\sin{x}$ is $\cos{x}$
@SanjiH, $$\lim_{z\to x}\dfrac{\sin(z-x)/2}{(z-x)/2}=1,$$ right?
Apr
17
comment Is it possible to calculate for example $\int_{0}^{1} x \mathrm{d}2x$
Try setting $2x=u$
Apr
17
comment Given $\frac{\sin(A - B)}{\sin(A+B)} = \frac57$, show $\tan A = 6 \tan B$
@user2650277, Not sure why? Then separate out $\sin A\cos B, \cos A\sin B$
Apr
17
comment How do I integrate this expression?
@Vizuna, Differentiate both sides wrt $x$