Question

Simplify $\tan^{-1}\Big[\frac{\cos x-\sin x}{\cos x+\sin x}\Big]$, where $x<\pi$

score 140 · Answer 1 · 2026-03-24 20:42:37

Simplify $\tan^{-1}\Big[\frac{\cos x-\sin x}{\cos x+\sin x}\Big]$, where $x<\pi$

Published on 24 Mar 2026 - 20:42

score 376 · Answer 2 · 2018-01-29 17:18:16

Find and proof the exact values to the equations $\sin(\pi/3), \cos(\pi/3), \sin(\pi/6), \cos(\pi/6)$ using $\sin(3x)=3\sin(x)-4\sin^3(x)$

score 210 · Answer 3 · 2026-03-25 08:03:57

210

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Complex numbers - $z^{2} = 4i$

Published on 25 Mar 2026 - 8:03

score 71 · Answer 4 · 2018-01-29 20:13:46

71

Views

Prove the following statements without using induction

Published on 29 Jan 2018 - 20:13

score 5.9k · Answer 5 · 2026-03-26 07:37:34

5.9k

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Sine wave plot using Matlab

Published on 26 Mar 2026 - 7:37

score 40 · Answer 6 · 2026-03-28 06:59:45

40

Views

Probability for all pairs $(x,y)$ with $x,y\in{[0,1]}$ that $\theta= \cos^{-1}\frac{-y^2+y-x^2}{\sqrt{x^2+(y-1)^2}\sqrt{x^2+y^2}} < 90^\circ$

Published on 28 Mar 2026 - 6:59

score 48 · Answer 7 · 2026-03-25 15:47:24

48

Views

$2\cos^2(3x)+5\cos(3x)−3<0$ solving for inequality

Published on 25 Mar 2026 - 15:47

score 98 · Answer 8 · 2026-03-24 20:47:47

98

Views

Minimum value of $(a+1)(b+1)$

Published on 24 Mar 2026 - 20:47

score 37 · Answer 9 · 2018-01-30 04:18:27

37

Views

Any techniques for finding integer values of a trigonometric expression?

Published on 30 Jan 2018 - 4:18

score 61 · Answer 10 · 2018-01-30 08:50:01

61

Views

Value of $\sec^2 a+2\sec^2 b$

Published on 30 Jan 2018 - 8:50

score 298 · Answer 11 · 2026-03-25 17:40:40

298

Views

Finding all solutions of $x$ in $\sin(\pi x)+x=0$.

Published on 25 Mar 2026 - 17:40

score 283 · Answer 12 · 2026-03-20 04:40:12

283

Views

Compute the period of this function $f(x)=7+3\cos{(\pi x)}-8\sin{(\pi x)}+4\cos{(2\pi x)}-6\sin{(2\pi x)}$

Published on 20 Mar 2026 - 4:40

score 54 · Answer 13 · 2018-01-30 13:21:33

54

Views

Trigonometric equation without graphs

Published on 30 Jan 2018 - 13:21

score 410 · Answer 14 · 2026-03-25 01:41:16

410

Views

Find the maximum area of a triangle given angle and opposite side

Published on 25 Mar 2026 - 1:41

score 316 · Answer 15 · 2026-03-24 20:46:41

316

Views

Proving that $\cos^{-1}\frac{4}{5}+\cos^{-1}\frac{12}{13}=\cos^{-1}\frac{33}{65}$

Published on 24 Mar 2026 - 20:46

List Question

Simplify $\tan^{-1}\Big[\frac{\cos x-\sin x}{\cos x+\sin x}\Big]$, where $x<\pi$

Find and proof the exact values to the equations $\sin(\pi/3), \cos(\pi/3), \sin(\pi/6), \cos(\pi/6)$ using $\sin(3x)=3\sin(x)-4\sin^3(x)$

Complex numbers - $z^{2} = 4i$

Prove the following statements without using induction

Sine wave plot using Matlab

Probability for all pairs $(x,y)$ with $x,y\in{[0,1]}$ that $\theta= \cos^{-1}\frac{-y^2+y-x^2}{\sqrt{x^2+(y-1)^2}\sqrt{x^2+y^2}} < 90^\circ$

$2\cos^2(3x)+5\cos(3x)−3<0$ solving for inequality

Minimum value of $(a+1)(b+1)$

Any techniques for finding integer values of a trigonometric expression?

Value of $\sec^2 a+2\sec^2 b$

Finding all solutions of $x$ in $\sin(\pi x)+x=0$.

Compute the period of this function $f(x)=7+3\cos{(\pi x)}-8\sin{(\pi x)}+4\cos{(2\pi x)}-6\sin{(2\pi x)}$

Trigonometric equation without graphs

Find the maximum area of a triangle given angle and opposite side

Proving that $\cos^{-1}\frac{4}{5}+\cos^{-1}\frac{12}{13}=\cos^{-1}\frac{33}{65}$

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