Question

If $\cos\theta=\frac{\cos\alpha+\cos \beta}{1+\cos\alpha\cos\beta}$, then prove that one value of $\tan(\theta/2)$ is $\tan(\alpha/2)\tan(\beta/2)$

score 752 · Answer 1 · 2026-04-15 18:47:31

If $\cos\theta=\frac{\cos\alpha+\cos \beta}{1+\cos\alpha\cos\beta}$, then prove that one value of $\tan(\theta/2)$ is $\tan(\alpha/2)\tan(\beta/2)$

score 988 · Answer 2 · 2026-04-15 09:31:57

988

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General solution to $\sin \alpha + \sin \beta$ and $\cos \alpha + \cos \beta$?

Published on 15 Apr 2026 - 9:31

score 2.9k · Answer 3 · 2026-04-17 03:54:22

2.9k

Views

Shouldn't tan(x) be a continuous function

Published on 17 Apr 2026 - 3:54

score 1.4k · Answer 4 · 2026-04-16 12:48:35

1.4k

Views

Error evaluating $ \lim_{x\to 0}\frac{x-\tan x}{x^3} $

Published on 16 Apr 2026 - 12:48

score 129 · Answer 5 · 2026-04-17 12:52:27

129

Views

If $\tan(x_1) \cdots\tan(x_n)=1$ for acute $x_i$, then does it follow that $\cos(x_1)+\cdots+\cos(x_n) \leq n\sqrt{2}/2$?

Published on 17 Apr 2026 - 12:52

score 139 · Answer 6 · 2026-04-16 01:32:23

139

Views

Proving $\int_0^\infty x^ne^{-tx}\frac{\sin x}xdx=\frac{\sin n\theta}{(1+t^2)^{n/2}}(n-1)!$, where $\theta=\arcsin\frac1{\sqrt{1+t^2}}$

Published on 16 Apr 2026 - 1:32

score 51 · Answer 7 · 2026-04-12 10:19:09

51

Views

Determine the range of a function

Published on 12 Apr 2026 - 10:19

score 62 · Answer 8 · 2026-04-11 06:50:39

62

Views

How can I find the 3D rotation angle of an isoceles trapezoid?

Published on 11 Apr 2026 - 6:50

score 93 · Answer 9 · 2026-04-09 00:56:21

93

Views

Based on geometry, Triangle

Published on 09 Apr 2026 - 0:56

score 92 · Answer 10 · 2026-04-16 00:54:47

92

Views

Decide all solutions to the following trigonometric equation: $\sin \left( 4\,x \right) =\cos \left( 3\,x \right).$ in the interval $[0, 2π[ $.

Published on 16 Apr 2026 - 0:54

score 86 · Answer 11 · 2026-04-15 22:14:06

Simplifying $\frac{{\sum_{i=1}^{i=n}}1+\tan^2\theta_i}{{\sum_{i=1}^{i=n}}1+\cot^2\theta_i}$, where $\theta_i = \frac{2^{i-1}\pi}{2^n+1}$

score 69 · Answer 12 · 2026-04-11 14:49:47

69

Views

Finding equidistant point using law of cosine/sine

Published on 11 Apr 2026 - 14:49

score 45 · Answer 13 · 2026-04-14 09:28:50

45

Views

Find the coefficient $c$ so the equation is even

Published on 14 Apr 2026 - 9:28

score 71 · Answer 14 · 2026-04-12 08:25:06

71

Views

Trigonometry Equations (Sum to Product)

Published on 12 Apr 2026 - 8:25

score 138 · Answer 15 · 2026-04-15 22:29:02

138

Views

If $\tan{\frac{x}{2}}=\csc x - \sin x$, then find the value of $\tan^2{\frac{x}{2}}$.

Published on 15 Apr 2026 - 22:29

List Question

If $\cos\theta=\frac{\cos\alpha+\cos \beta}{1+\cos\alpha\cos\beta}$, then prove that one value of $\tan(\theta/2)$ is $\tan(\alpha/2)\tan(\beta/2)$

General solution to $\sin \alpha + \sin \beta$ and $\cos \alpha + \cos \beta$?

Shouldn't tan(x) be a continuous function

Error evaluating $ \lim_{x\to 0}\frac{x-\tan x}{x^3} $

If $\tan(x_1) \cdots\tan(x_n)=1$ for acute $x_i$, then does it follow that $\cos(x_1)+\cdots+\cos(x_n) \leq n\sqrt{2}/2$?

Proving $\int_0^\infty x^ne^{-tx}\frac{\sin x}xdx=\frac{\sin n\theta}{(1+t^2)^{n/2}}(n-1)!$, where $\theta=\arcsin\frac1{\sqrt{1+t^2}}$

Determine the range of a function

How can I find the 3D rotation angle of an isoceles trapezoid?

Based on geometry, Triangle

Decide all solutions to the following trigonometric equation: $\sin \left( 4\,x \right) =\cos \left( 3\,x \right).$ in the interval $[0, 2π[ $.

Simplifying $\frac{{\sum_{i=1}^{i=n}}1+\tan^2\theta_i}{{\sum_{i=1}^{i=n}}1+\cot^2\theta_i}$, where $\theta_i = \frac{2^{i-1}\pi}{2^n+1}$

Finding equidistant point using law of cosine/sine

Find the coefficient $c$ so the equation is even

Trigonometry Equations (Sum to Product)

If $\tan{\frac{x}{2}}=\csc x - \sin x$, then find the value of $\tan^2{\frac{x}{2}}$.

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