Sum of Geometric Sequence
S_n=\dfrac{a_1(1-::r::^n)}{1-::r::}
Sine of the sum of two angles formula
\sin (\alpha +\beta ) = \sin \alpha\cos \beta +\cos \alpha \sin \beta
Cosine of the difference of two angles formula
\cos(\alpha -\beta ) = \cos \alpha\cos \beta +\sin \alpha \sin \beta
The double angle cosine formula
\cos 2\alpha =2 \cos^2 \alpha - 1
The double angle cosine formula
\cos 2\alpha = \cos^2 \alpha - \sin^2 \alpha
The double angle sine formula
\sin 2\alpha = 2 \sin \alpha\cos \alpha
Tangent of the difference of two angles formula
\tan(\alpha -\beta) = \dfrac{\tan \alpha - \tan \beta }{1+\tan \alpha\tan \beta}
Tangent of the sum of two angles
\tan(\alpha+\beta) = \dfrac{\tan \alpha + \tan \beta }{1-\tan \alpha\tan \beta}
Factor formula - the difference of sine of two angles
\sin \alpha - \sin \beta = 2\cos\dfrac{\alpha +\beta }{2} \sin\dfrac{\alpha -\beta }{2}
Factor Formula - the sum of sine of two angles
\sin \alpha + \sin \beta = 2\sin\dfrac{\alpha +\beta }{2} \cos\dfrac{\alpha -\beta }{2}
Factor formula - the difference of cosine of two angles
\cos \alpha - \cos \beta = -2\sin\dfrac{\alpha +\beta }{2} \sin\dfrac{\alpha -\beta }{2}
Factor fomula - the sum of cosine of two angles
\cos \alpha + \cos \beta = 2\cos\dfrac{\alpha +\beta }{2} \cos\dfrac{\alpha -\beta }{2}
Product formula - cosine and sine
\cos \alpha\sin \beta = \dfrac{1}{2} [\sin(\alpha+\beta ) - \sin(\alpha - \beta) ]
Product formula - sine anf cosine
\sin \alpha\cos \beta = \dfrac{1}{2} [\sin(\alpha+\beta ) +\sin(\alpha - \beta) ]
Product formula - sine of two angles
\sin \alpha\sin \beta = \dfrac{1}{2} [\cos(\alpha-\beta ) - \cos(\alpha + \beta) ]