Question

About proof: $\cot^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right)=\frac x2$

score 1.4k · Answer 1 · 2018-12-01 12:45:20

1.4k

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About proof: $\cot^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right)=\frac x2$

Published on 01 Dec 2018 - 12:45

score 269 · Answer 2 · 2018-12-01 16:55:27

269

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Simplifying $\frac{\cot(34^\circ)\sin(44^\circ)}{\sin(22^\circ)\sin(56^\circ)} $

Published on 01 Dec 2018 - 16:55

score 82 · Answer 3 · 2026-04-13 08:21:58

82

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Values of $x$ satisfying $\sin x\cdot\cos^3 x>\sin^3x\cdot\cos x$

Published on 13 Apr 2026 - 8:21

score 520 · Answer 4 · 2026-04-13 22:57:00

520

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Simple trigonometry: negative cos and sin

Published on 13 Apr 2026 - 22:57

score 54 · Answer 5 · 2026-04-13 08:17:29

54

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Show that $\lvert\frac{1}{x} \sin x-\sum _{k=0}^n (-1)^k\frac{x^{2k}}{(2k+1)!}\rvert\leq\frac{|x|^{2n+1}}{(2n+2)!}$

Published on 13 Apr 2026 - 8:17

score 186 · Answer 6 · 2018-12-02 12:44:53

186

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What is the radius 1 in unit circle

Published on 02 Dec 2018 - 12:44

score 183 · Answer 7 · 2026-04-13 05:26:56

183

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Let $\Delta ABC$ be a right triangle. Prove that $\angle BEH=\angle HCI$.

Published on 13 Apr 2026 - 5:26

score 1.8k · Answer 8 · 2018-12-02 16:54:16

1.8k

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Given $\tan\alpha=2$, evaluate $\frac{\sin^{3}\alpha - 2\cos^{3}\alpha + 3\cos\alpha}{3\sin\alpha +2\cos\alpha}$

Published on 02 Dec 2018 - 16:54

score 946 · Answer 9 · 2026-04-13 19:49:09

946

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Solve, $\sin(2x) = \cos(x)$, on the interval $[0, 2\pi)$.

Published on 13 Apr 2026 - 19:49

score 120 · Answer 10 · 2026-04-13 16:56:17

120

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Prove that $BH=AH$

Published on 13 Apr 2026 - 16:56

score 501 · Answer 11 · 2026-04-09 02:42:17

501

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A curious geometry problem: Find the $\angle OBC$

Published on 09 Apr 2026 - 2:42

score 758 · Answer 12 · 2018-12-03 00:17:29

758

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Showing that $\int_0^\pi\frac{\cos n\theta}{\cos\theta-\cos\theta_0}d\theta=\pi\frac{\sin n\theta_0}{\sin\theta_0}$

Published on 03 Dec 2018 - 0:17

score 82 · Answer 13 · 2018-12-03 00:57:52

82

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Rewriting $\sin(x+\frac {\pi} {6})\cos(x)$ as $\frac {1} {4}(2\sin(2x+\frac {\pi} {6})+1)$

Published on 03 Dec 2018 - 0:57

score 192 · Answer 14 · 2026-04-12 17:05:06

192

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Given $y = A\cos(kt) + B\sin(kt)$, where $A, B, k$ are constants, prove that $y^{(2)} + (k^2)y = 0$

Published on 12 Apr 2026 - 17:05

score 106 · Answer 15 · 2026-04-12 03:31:18

106

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iterated double angle formula -- speed of convergence

Published on 12 Apr 2026 - 3:31

List Question

About proof: $\cot^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right)=\frac x2$

Simplifying $\frac{\cot(34^\circ)\sin(44^\circ)}{\sin(22^\circ)\sin(56^\circ)} $

Values of $x$ satisfying $\sin x\cdot\cos^3 x>\sin^3x\cdot\cos x$

Simple trigonometry: negative cos and sin

Show that $\lvert\frac{1}{x} \sin x-\sum _{k=0}^n (-1)^k\frac{x^{2k}}{(2k+1)!}\rvert\leq\frac{|x|^{2n+1}}{(2n+2)!}$

What is the radius 1 in unit circle

Let $\Delta ABC$ be a right triangle. Prove that $\angle BEH=\angle HCI$.

Given $\tan\alpha=2$, evaluate $\frac{\sin^{3}\alpha - 2\cos^{3}\alpha + 3\cos\alpha}{3\sin\alpha +2\cos\alpha}$

Solve, $\sin(2x) = \cos(x)$, on the interval $[0, 2\pi)$.

Prove that $BH=AH$

A curious geometry problem: Find the $\angle OBC$

Showing that $\int_0^\pi\frac{\cos n\theta}{\cos\theta-\cos\theta_0}d\theta=\pi\frac{\sin n\theta_0}{\sin\theta_0}$

Rewriting $\sin(x+\frac {\pi} {6})\cos(x)$ as $\frac {1} {4}(2\sin(2x+\frac {\pi} {6})+1)$

Given $y = A\cos(kt) + B\sin(kt)$, where $A, B, k$ are constants, prove that $y^{(2)} + (k^2)y = 0$

iterated double angle formula -- speed of convergence

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