01 Trignometric

Last Updated: 2 years ago2023-01-25 ; Contributors: AhmedThahir
Rule
Product 2sin⁡xcos⁡y2 \sin x \cos y sin⁡(x+y)+sin⁡(x−y)\sin(x+y) + \sin(x-y)
2cos⁡xsin⁡y2 \cos x \sin y sin⁡(x+y)−sin⁡(x−y)\sin(x+y) - \sin(x-y)
2cos⁡xcos⁡y2 \cos x \cos y cos⁡(x+y)+cos⁡(x−y)\cos(x+y) + \cos(x-y)
2sin⁡xsin⁡y2 \sin x \sin y cos⁡(x−y)−cos⁡(x+y)\cos(x-y) - \cos(x+y)
Sum sin⁡C+sin⁡D\sin C + \sin D 2sin⁡(C+D2)cos⁡(C−D2)2 \sin \left( \frac{C+D}{2} \right) \cos \left( \frac{C-D}{2} \right)
sin⁡C−sin⁡D\sin C - \sin D 2cos⁡(C+D2)sin⁡(C−D2)2 \cos \left( \frac{C+D}{2} \right) \sin \left( \frac{C-D}{2} \right)
cos⁡C+cos⁡D\cos C + \cos D 2cos⁡(C+D2)cos⁡(C−D2)2 \cos \left( \frac{C+D}{2} \right) \cos \left( \frac{C-D}{2} \right)
\(\cos C - \cos D\) \(-2 \sin \left( \frac{C+D}{2} \right) \sin \left( \frac{C-D}{2} \right)\)
\(\tan(x+y)\) \(\frac{\tan x + \tan y}{1 - \tan x \tan y}\)
\(\tan(x-y)\) \(\frac{\tan x - \tan y}{1 + \tan x \tan y}\)
Double \(\sin 2x\) \(2 \sin x \cos x\) \(\frac{2 \tan x}{1 + \tan^2 x}\)
\(\cos 2x\) \(\cos^2 x - \sin^2 x\)
\(2\cos^2 x - 1\)
\(1 - 2 \sin^2 x\)		 \(\frac{1-\tan^2 x}{1 + \tan^2 x}\)
\(\tan 2x\) \(\frac{2 \tan x}{1 - \tan^2 x}\)
\(\cot 2x\) \(\frac{\cot^2 x - 1}{2 \cot x}\)
Triple \(\sin 3x\) \(3 \sin x - 4\sin^3 x\)
\(\cos 3x\) \(4\cos^3 x - 3\cos x\)
\(\tan 3x\) \(\frac{3\tan x - \tan^3 x}{1 - 3 \tan^2 x}\)
\(\cot 3x\) \(\frac{3 \cot x - \cot^3 x}{1 - 3 \cot^2 x}\)
Half \(\tan \frac{x}{2}\) \(\text{cosec }x - \cot x\) \(\sqrt{\frac{1-\cos x}{1+\cos x}}\)
\(\cot \frac{x}{2}\) \(\text{cosec }x + \cot x\) \(\sqrt{\frac{1+\cos x}{1-\cos x}}\)

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