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Oct
14
comment Showing Discrete Sum Equality
math.stackexchange.com/questions/591350/…
Oct
14
answered How to simplify this alternating modulo expression?
Oct
14
comment Show that the common tangents to circles $x^2+y^2+2x=0$ and $x^2+y^2-6x=0$ …
Related : math.stackexchange.com/questions/211538/… ??
Oct
14
revised Show that $2\cos(x)$ is equal to $2\cos(2x)\sec(x)+\sec(x)\tan(x)\sin(2x)$
added 6 characters in body; edited title
Oct
14
answered Show that $2\cos(x)$ is equal to $2\cos(2x)\sec(x)+\sec(x)\tan(x)\sin(2x)$
Oct
14
answered Is $\frac{4n^2+4n+1}{8}$ an integer for any $n\in \mathbb{N}$?
Oct
13
answered Solution to some confusing complex equation
Oct
13
answered Equation of circle in terms of length of arc above $x$-axis
Oct
13
answered Proving a Recursion Using Induction
Oct
13
comment Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$
@Danxe, From my answer, $$I=\int_0^\pi(\pi-x)f(\sin x)dx=\pi\int_0^\pi f(\sin x)dx-\int_0^\pi xf(\sin x)dx$$ $$\implies I=\pi\int_0^\pi f(\sin x)dx-I$$
Oct
13
comment Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$
@Danxe, Setting $a+b-x=u,-dx=du$ $$\int_a^bf(x)dx=\int_b^af(a+b-u)(-du)=-\int_a^bf(a+b-u)du$$ Now, $$\int_a^bf(a+b-u)du=\int_a^bf(a+b-x)dx$$ Finally, $$\int_c^df(x)dx=-\int_d^cf(x)dx$$
Oct
13
comment Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$
@Danxe, Set $a+b-x=u$ in the left hand side
Oct
13
answered Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$
Oct
13
answered Substitution method for solving recurrences piece wise function
Oct
13
comment Trigonometry equation with arctan
@XMLParsing, How about this?
Oct
13
answered Trigonometry equation with arctan
Oct
13
answered Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
Oct
13
answered How to solve $\frac{15!}{(x-1)!(16-x)!}=\frac{15!}{(2x+1)!(14-2x)!}$ for $x$?
Oct
12
answered $\lim_{x\to\infty} \frac{x}{\sqrt{9x^2 +x} -3}$
Oct
12
comment How to find all solutions of $\tan(x) = 2 + \tan(3x)$ without a calculator?
@user183782, How about this?