Show $\frac{\sin x_1\sin x_2\cdots\sin x_n}{\sin(x_1+x_2)\sin(x_2+x_3)\cdots\sin(x_n+x_1)}\le\frac{\sin^n(\pi/n)}{\sin^n(2\pi/n)}$, for $\sum x_i=\pi$

score 135 · Answer 10 · 2026-04-13 19:16:35

135

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Find the value of $x$, if both angles are acute and $\cot (3x-40) = \tan (2x+100)$

Published on 13 Apr 2026 - 19:16

score 46 · Answer 11 · 2026-04-16 17:28:42

46

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Finding $\lim_{n\rightarrow \infty}\sum^{n}_{r=1}\cot^{-1}\bigg(\frac{n^2(r^2+r+1)+2n+1}{n^2+n}\bigg)$

Published on 16 Apr 2026 - 17:28

score 140 · Answer 12 · 2026-04-16 08:17:22

140

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How to solve $x = 45 \cos(x)$

Published on 16 Apr 2026 - 8:17

score 61 · Answer 13 · 2026-04-16 17:44:25

61

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How to draw this triangle?

Published on 16 Apr 2026 - 17:44

score 80 · Answer 14 · 2026-04-13 07:34:20

80

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How are different senses of the term 'harmonic' related to each other?

Published on 13 Apr 2026 - 7:34

score 171 · Answer 15 · 2026-04-14 00:56:20

171

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How do you integrate $\int_{0}^{\infty}\frac{a\cos{(cx)}}{a^2+x^2}dx$?

Published on 14 Apr 2026 - 0:56

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Find the value of $x$, if both angles are acute and $\cot (3x-40) = \tan (2x+100)$

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